Aha, my favourite, ska and punk. Get ready:
Sonic Boom Six - http://www.youtube.com/watch?v=v1XalWiJt6g, http://www.youtube.com/watch?v=kfBy_me9ij4, http://www.youtube.com/watch?v=YmUlaDtrGqc (one of my favourite bands)
Left?ver Crack - http://www.youtube.com/watch?v=GZKJwdJRbCo
Random Hand - http://www.youtube.com/watch?v=VcJWEqTie38, http://www.youtube.com/watch?v=IdH2JenalMM, http://www.youtube.com/watch?v=zrUsvbJbVxU
Capdown - http://www.youtube.com/watch?v=K10-JjPXNaw, http://www.youtube.com/watch?v=9PQV-j1JZ7c
King Prawn - http://www.youtube.com/watch?v=9Q7CycUkDQU, http://www.youtube.com/watch?v=k2Aj4Eg0imA (King Prawn and Capdown are legends in the British ska underground)
Big D and the Kids Table - http://www.youtube.com/watch?v=D8oM_-K9rXY, http://www.youtube.com/watch?v=qsEKXKjPRWY, http://www.youtube.com/watch?v=adglbndu-6o
Rancid - http://www.youtube.com/watch?v=DhKHAopx7D0
Tim Armstrong - http://www.youtube.com/watch?v=0zmIR1aAGYE
NoFX - http://www.youtube.com/watch?v=6axOY4PBusk, http://www.youtube.com/watch?v=TWrlbRdJsSE, http://www.youtube.com/watch?v=krZyeldj7tQ
Stand Out Riot - http://www.youtube.com/watch?v=FxoH2pMd_eg
AWarAgainstSound - http://www.youtube.com/watch?v=IXkbQmG7dmA (the album this is taken from - a three way split between Stand Out Riot, AWAS and Sense of Urgency - is one of the best skacore albums you will ever hear in your life)
Mouthwash - http://www.youtube.com/watch?v=jdgjJJhJOa0
The Skints - http://www.youtube.com/watch?v=eTRBjxBmUCY (probably the best British reggae/ska band around at the moment)
Bad Religion - http://www.youtube.com/watch?v=6XRt5cbNhUo, http://www.youtube.com/watch?v=12kcpP-8jfM, http://www.youtube.com/watch?v=v1PgiBpTtao
A Wilhelm Scream - http://www.youtube.com/watch?v=jGfWeOulgHs
The Selecter - http://www.youtube.com/watch?v=2wwSQa3XZfs, http://www.youtube.com/watch?v=ETTKzcIQTjU
The Creepshow - http://www.youtube.com/watch?v=Yu3Rfc9fr-0
Trash Talk - http://www.youtube.com/watch?v=AV1TeGIeMC4
The Suicide Machines - http://www.youtube.com/watch?v=7sENFugWIX4
The Aggrolites - http://www.youtube.com/watch?v=hi4Ys9CgSfE, http://www.youtube.com/watch?v=aYtnwPy410M
The Stooges - http://www.youtube.com/watch?v=BJIqnXTqg8I, http://www.youtube.com/watch?v=3mZ0sSStW6Y (take it back to the start...)
The Clash - http://www.youtube.com/watch?v=wqcizZebcaU
I haven't watched any of these videos because I don't have a million years of time, so apologies if any are low quality or have stupid fan animations or slideshows on them or something. Also, I didn't know how much you already knew, so there's some fairly obvious bands in there you probably have heard, but there's also loads that you probably wont, so do check 'em out

Also, a bunch of British bands which are awesome but not well known enough to have decent quality videos on YouTube (they might have MySpace pages or something though...):
The Hostiles, Dirty Revolution, Revenge of the Psychotronic Man, Broken Nose, ACiD DROP...