https://www.which.co.uk/money/banking/bank-accounts/best-and...
Top of the list (as it often has been for decades) is First Direct. This is a challenger bank in its own way - it was launched in 1989 to pioneer telephone banking, a disruptive technology at the time! It now has phone and internet banking, but still has no physical branches.
Monzo and Starling, the proper challenger banks, are also rated very highly, taking the second and third spots.
Behind them are some somewhat unconventional banks:
Nationwide is a building society rather than a bank; functionally it's a bank, but it's owned by its customers, rather than by investors. Dates to the 19th century, has many branches, very boring really. My mum banks with them, and she doesn't complain.
Marks & Spencer is an upmarket department store (i swear by their lambswool socks!) which branched out into banking a while ago.
Metro Bank is a perfectly normal high street bank, with branches and so on, but it was founded in 2010. Apparently the last time a new bank was founded before that was 150 years earlier.
The Co-operative Bank is, as the name suggests, a co-operative. It's a bit like a building society, but not. I bank with them. Their website is terrible and their phone customer service has been slashed (although when you do get through to someone, they're great).
Only then do you get to Barclays, which is a classic high street bank - founded in the 17th century, branches in every town, full service, investment banking arm, rigs LIBOR, etc.