Yes there is, perhaps, about 10X more variety in British accents than in American.
There are some I think of as rather ugly. They tend to coincide with industrial regions, well now post-industrial. Some might therefore impute me snobbery but on the other hand I like the West Country accent which other snobs consider yokelish country bumpkin. My favorite accent is the Welsh. But it is also a spirit and way of saying things and there is more than just sound involved in all these accents, and personal history also in one's likes. Welsh accent would not do if everybody spoke it because it involves, so say phoneticists, a 'phonetic simplification' with respect to standard English.
The regional accents were in decline but have made a comeback. The last ten or so years have seen the diffusion of something called 'Estuary English' which, nearest description I can manage, has a base of a kind of lazy diluted Cockney after diasporisation through South ('Sarf') London and Essex (

) with various additions including American plus whatever mid-Atlantic publicityspeak is imagined as such, Caribbean, borrowings from Geek

acronymised and txted; the salad cream smothering this mishmash of linguistic fastfood is the desire to at all costs sound streetwise.