You know what, reading back I don't think anyone's mentioned The Jam!
If I was giving my top ten fave British bands it would likely be different but I think the OP's question should be based on chronological importance so my top ten in that respect would be:
The Shadows with or without Cliff they were the first guitar hero band in the UK.
The Beatles changed everything not just in the UK but worldwide.
The Rolling Stones along with the Beatles good boys image the Stones had the opposite image.
The Who amalgamated the influences of the above and created a whole new tribe in the mods.
Cream took virtuosity to another level and did away with the three minute track length
Fairport Convention took folk music and electrified it.
David Bowie creator of artrock.
The Police not personally a big fan but they did take that reggae thing and turn it into something new.
The Clash the Stones of the punk era
The Jam the Beatles of the punk era.