Some suggestions:

Trainspotting

The Monty Python films, Life of Brian and Holy Grail.

The Full Monty

The Italian Job (the original, not the rubbish American remake)

Dead Man's Shoes

Kind Hearts and Coronets (this is a much older film but I think it is fantastic).

Withnail and I

A Clockwork Orange

Billy Elliot

The Long Good Friday

Kes (Very very strong regional accents in this one, but it is really good).

If you like Football Factory, there is another similar film called Green Street. I think both of those films are terrible but you're welcome to watch it and form your own opinion :)

No, Teytan. I take note! 

Don't say that you haven't seen Snatch!!

I would like to add Shallow Grave. 

Ah OK I understand. But it's definitely worth a watch if you can find it with subtitles. A lot of the characters have strong London accents so without subtitles I can see how it would be hard to follow.