This website gives all the details for the main motorbike racing in Ireland and englandirishroadracing.co.uk
If you can get to one of these races you won't be disapointed these are racers who won't go onto MotoGP because it's "for pussys" bispite the wages in GP and the fact that someone dies at nearly every road race.
The other big sport in the UK is British Touring car www.btccpages.com
more or less a contact sport.
Then there's rally driving ukmotorsport.com
There are TONS of small rallys through Ireland and England and while you'll get to see some good one's in the UK nothing compares to the tiny Irish roads with ditches. Seeing a subaru doing the ton over a 800 year old bridge then straight into a tight right going up over a hill can't be beat.
Go-carting, formula ford and formula 3000 are other ones to look out for too.