I don't even know if I would go that far, especially taking into account great music since say 2000.
Outside of Kid A and Back to Black, I'm struggling to name any 'modern classics' that have come out of the UK this millennium. A lot of the best albums of recent times have been American like To Pimp a Butterfly, White Blood Cells, Elephant, Is This It, My Beautiful Dark Twisted Fantasy, The Black Album, The Blueprint, Sound of Silver, Yankee Hotel Foxtrot, MMLP, XXX all came out of America
For the UK there was plenty of Modern Classics. Whatever People Say I Am That's What I'm Not by Arctic Monkeys was voted as the 19th Best album of all time by NME which should show how highly people consider it, hell the first two singles from the album went straight to No.1 and the album was the fastest selling British debut album ever which are accomplishments basically unheard of for an indie band out of Sheffield. That along with Favourite Worst Nightmare are both considered modern classics, I don't really think people consider White Blood Cells as a modern classic, Is This It is undeniably one but even Elephant I'd have a hard time justifying that.
Plus the UK scene had a big resurgence recently so albums recently released are yet to be remembered as modern classics, plus a lot of being considered a modern classic is based on popularity an album like My Love Is Cool by Wolf Alice is amazing but isn't well known, albums from Kendrick Lamar for example are largely popular so will be viewed differently than a lot of smaller bands across the pond. And even to counter your point on hip hop London has been a hub for hip hop since the turn of the century and has produced some amazing artists like Stormzy for example.
And lets say for example there were no true "Modern Classics" from the UK since 2000 (Which I counter argue in a second but for example) then you would be ignoring how British artists basically put down the foundation for most genres as we know right now, pretty much every Rock genre out there can be traced back to The Beatles or The Rolling Stones.
Anyway here are some albums I'd consider Modern Classics:
Whatever People Say I Am, Favourite Worst Nightmare both by Arctic Monkeys
My Love Is Cool by Wolf Alice
The Balcony by Catfish and The Bottlemen
For Crying Out Loud and Self Titled album by Kasabian
Royal Blood Self Titled album
Franz Ferdinand Self Titled Album
The Kooks: Inside In/Inside Out
Everything You've Come To Expect by The Last Shadow Puppets
Don't Believe The Truth by Oasis
Blackstar by David Bowie
That is just off the top of my head what I'd consider modern classics, I'm sure if I went through my records and my spotify I could find even more and then we're not even talking about genres I don't personally listen to much. You could say Royal Blood is debatable but the critical acclaim surrounding it leads me to think it will be highly regarded. Yeah sure the UK scene has struggled a bit particularly after Oasis split up but the post punk revival scene in the mid 2000s as well as newer bands such as Wolf Alice, Catfish and The Bottlemen etc and then I didn't even talk about Ed Sheeran who has taken the world by absolute storm I mean he headlined Glastonbury with just an acoustic guitar and I'll be honest his albums are pretty great and I think Divide will be considered a modern pop classic. Even bands like The 1975 who I think are absolute garbage will probably be held in high regard in the future due to their current popularity. I love The Strokes as much as the next guy but I definitely think Whatever People Say I Am is on equal par with Is This It, they are shockingly similar showing The Strokes influence on AM's work.
The Strokes and Arctic Monkeys are very similar probably why I adore both of them, they both influenced an entire generation of musicians. Arctic Monkeys may have found more popularity but that is just part of the tragedy of The Strokes, through many factors including things like Ablert's heroin abuse The Strokes were never able to capitalise on the momentum of Is This It, Room on Fire is an excellent album but the harsh drop in quality going into First Impressions Of Earth is hard to deny.
Edit: I forgot to include The Libertines, one of the best bands to ever come out of the UK. Self titled would definitely be a Modern Classic.