Great OP, this thread is one of them most personally exciting I've seen in a few years of lurking OT. I can see what you mean about some of the E6 people, but everything I've read or heard most of the guys (outside of modern Kevin Barnes) is that they're some of the sweetest, most sincere dudes. I think their naming convention has more to do with wanting to preserve what's their idea of a tradition of psych-pop weirdness and engaging in things in a way that feels real and fun to them, not a desire to be hipper than thou. Maybe I'm an apologist, but again, heard nothing but good things about 90% of those people.
Anyway, love this kind of music and could probably dig up a few bands that some of you guys could get into. This might get a little bit long but, eh, why not, I'm not sleeping anytime soon.
As far as E6 stuff goes, The Minders and Circulatory System deserve a mention.
The Minders - Hooray For Tuesday - "Yeah Yeah Yeah":
http://www.youtube.com/watch?v=YzqN_gp0644
Unfortunately, this is kind of a "minor" Minders song, but there's really slim pickings on YouTube. The albums Hooray For Tuesday and Bright, Guilty World are both solid 60s pop through and through, though.
Circulatory System - Circulatory System - "Joy":
http://www.youtube.com/watch?v=a_jidcdzXuU
This is Will Cullen Hart's (of OTC) new band. It's a little darker and more blatantly psychedelic than most of the things talked about so far, but this album is amazing and unlike anything else I've heard. It takes some time to reveal it's charms, though.
XTC - Skylarking - "Ballet For A Rainy Day":
http://www.youtube.com/watch?v=a11mwm0rXX4
This album is one of the best strongly 60s inspired albums of the 80s. Produced by Todd Rundgren. Check out their side project The Dukes of Stratosphear for even more Beatles-esque tunes.
Bikeride - Morning Macumba - "Knees on Top":
http://www.myspace.com/bikeride
I urge anyone interested in well-crafted 60s/psych/whatever pop to check out this tune. They were a band that were never really given their due and their singer quite tragically passed away in 2008. Their earlier stuff borders on twee but their last few releases are very accomplished Beach Boys-esque pop.
Chris Stamey - DIY Come Out and Play - "The Summer Sun":
http://www.youtube.com/watch?v=84_uiSGcin0
This is Chris Stamey of The dB's, who have more in common with Big Star than the Beatles, but this is just a perfectly constructed pop song, definitely Anglophilic and a shining moment for power pop.
Beulah - Yoko - "Landslide Baby":
http://www.youtube.com/watch?v=z8S3k2TWaJo
Another great E6 band, but mostly only by association, they were very little involved in any real collective. They had three albums of sunshiney, expertly-crafted pop before releasing their final album,
Yoko, which was darker but also their most accomplished work.
Butterfly Child - Soft Explosives - "Drunk on Beauty":
http://www.youtube.com/watch?v=BorhEgWMOog
To be honest, I'm no expert on this band. I found out about them on some likely now extinct music website almost a decade ago, and have never fully explored their catalog. There's a few tracks by them that I go back to, though, and this is one of them.
Ambulance LTD. - Ambulance LTD. - "Stay Where You Are":
http://www.youtube.com/watch?v=1plARzmiX5k
Honestly, I'm not sure how Beatles-influenced this is, but it's some great guitar pop and one of the dudes worked with John Cale for a while so that gives them some 60s pop cred. I sat on this album for a while before getting into it but it's indispensable now.
The Deadly Snakes - Porcella - "Gore Veil":
http://www.youtube.com/watch?v=tj2vSLRpYj4
This band has more in common with The Rolling Stones than the Beatles, but I don't think that that warrants their exclusion from this thread. One of the best garage rock albums I've heard in the past few years.
The Delgados - Hate - "All You Need Is Hate":
http://www.youtube.com/watch?v=NSMLx44DqFc
No need to explain the Beatles connection on this one, it says it all right there in the title. I have to say though, as great a song as this, you're doing yourself a disservice by listening to it on YouTube. It's bombastic and rich, aided by the production of David Fridmann, probably best known for produced a lot of the best Flaming Lips albums.
The Exploding Hearts - Guitar Romantic - "Sleeping Aides and Razor Blades":
http://www.youtube.com/watch?v=d1rS5V9mZHA
Probably the most rocking song I'll include in this post. It's a few degrees removed from pure Anglophilic, Beatles-esque pop, in that The Exploding Hearts are more of a direct descendant of power pop bands like Big Star, The dB's, The Replacements and the Nerves, but anyone who likes loud guitar, big hooks and a bit of a punk attitude should feel at home with this. Another sad story here, all but one of the members died in a car accident while on tour and they only managed to put out one proper album in their career.
The Glands - The Glands - "Swim":
http://www.youtube.com/watch?v=sn-Ip7HwWLE
I hate to reference a Pitchfork review, but they were right when they identified The Glands as a band of enthusiastic music nerds whose record collections probably outweighed their ambitions or proficiency, but regardless, their self-titled album is an eclectic, top-notch pop album.
Guided by Voices - Alien Lanes - "Game of Pricks":
http://www.youtube.com/watch?v=IlZlst4NBVw
Hands down my favorite band. Some people just don't "get it", maybe because of their endless catalog, or maybe because of their often primitive sound quality, but Robert Pollard has serious songwriting chops. "Game of Pricks" wouldn't sound out of place on an early Beatles album, and I mean that in the best possible way. That being said, their catalog does go in a lot of different directions, not all of them immediately accessible.
The Heavy Blinkers - The Night and I Are Still So Young - "The Night and I Are Still So Young":
http://www.youtube.com/watch?v=XEaz_Z7sZuA
This is richly orchestrated, compositionally nuanced pop in the vein of
Pet Sounds or The Carpenters. Just like the Carpenters, they can get a little bubblegummy at times, but usual lead vocalist Ruth Minnikin has a voice to melt glass, and it's so well put together. Another band/song/album that is not best enjoyed via YouTube.
The Green Pajamas - All Clues Lead to Megan's Bed - "Death By Poisoning":
http://www.youtube.com/watch?v=Uyf4-qsjTfs&feature=related
While not an hugely well-known band, I've always had the impression that there's a small, dedicated fanbase that believes that The Green Pajamas have made some of the finest psych-pop for at least a couple decades now. I don't know if I'd go that far, but this album is definitely worth a spin.
Lawrence Arabia - Chant Darling - "Apple Pie Bed":
http://www.youtube.com/watch?v=SgM74NERL_s
This is actually one of my favorite albums of the year. Definitely for fans of Gorky's Zygotic Mynci or Super Furry Animals, slightly off-kilter, fun, warm pop music.
The Left Banke - There's Going to Be a Storm - "Walk Away Renee":
http://www.youtube.com/watch?v=SqAh1dQu_pg&feature=related
The Left Banke has always been one of my favorite "B-tier" 60s pop bands. They were definitely onto something. Posting this song might be redundant, as it's rightfully considered a classic, but I'm sure a lot of GAFers have let it slip by them, until now.
Love - Forever Changes - "Alone Again Or":
http://www.youtube.com/watch?v=7yVBMUXr4xo
Maybe I'm straying a little too far, as this song is pretty far from Anglophilic. But it's pretty contemporary with the Beatles, and takes things in an entirely different direction. This song should serve as an introduction to what is now considered an essential album
The New Pornographers - Together - "Crash Years":
http://www.youtube.com/watch?v=_KZANuDcRO4
There are probably plenty of New Pornographers songs I could pick that are more appropriate for this thread, but the real point is that the New Pornographers (Neko Case, Destroyer's Dan Bejar and ringleader A. C. Newman) are a modern pop factory. Maybe what they most share with the Beatles is a professional-like commitment to crafting a perfect song without ever allowing it to come off as artifice or impersonal.
The Only Ones - The Only Ones - "Another Girl, Another Planet":
http://www.youtube.com/watch?v=VvO7HNQPFRI
I carry this band's torch with a dedication that really knows no match. Think Replacements or VU and you're on the right track. Their three albums are not to be missed, great guitars, great vocals, great writing, everything.
Pernice Brothers - Overcome by Happiness - "Overcome by Happiness":
http://www.youtube.com/watch?v=IF02KEfUCtc&feature=related
A little bit of a modern indie rock sheen with tinges of alt. country (hints of Joe Pernice's earlier band, The Scud Mountain Boys), The Pernice Brothers mostly traffic in shimmering but incredibly depressing guitar pop.
Phantom Buffalo - Take to the Hills - "Mrs. Connelly":
http://www.myspace.com/phantombuffalo
In my estimation they're one of the most criminally overlooked bands around. Not too dissimilar from the aforementioned Pernice Brothers in terms of sound (though they sometimes evocate Love), they rarely veer outside of a classically weird, psychedelic zone area that suits them just fine.
Sagittarius - Present Tense - "My World Fell Down":
http://www.youtube.com/watch?v=jU0Tfaluna0
A studio project of Gary Usher, Sagittarius is closest to the Zombies or the Beach Boys. I wish I could have found "You Know I've Found a Way" but this is more popular anyway. Great studio pop.
Sonny & The Sunsets - Tomorrow is Alright - "Too Young to Burn":
http://www.youtube.com/watch?v=Un2xYzvAqhw
This song is a recent obsession. Probably closest to The Violent Femmes or Johnathan Richman but I saw it in my iTunes and felt like anyone with an interest in any of the other stuff mentioned in this thread might get something out of it.
Teenage Fanclub - Bandwagonesque - "The Concept":
http://www.youtube.com/watch?v=rqYibZeafg8
This is an early 90s album, pretty reminiscent of the Byrds and (at other parts of the album) Big Star. I'm kind of running out of ways to say "pop music" at this point, so I'm going to call it good and try to better adhere to my policy of not talking music on GAF.
EDIT: But if anyone is interested I can go through some Nuggets comps, etc., and post some of them best tracks in the next few days.