Hi James.
I’m not in the Hull area so can’t give you names etc. However I have used agencies for work many times over the years, and am working for one now. So, some suggestions from my experience:
Try Google / Yellow Pages etc. to find agencies in the area, looking specifically for ones that specialize in drivers.
Sign up to two or three. That way at least one of them should be offering you work when you are available for it.
When you are working you will get to talk to other drivers, some will be agency, and they may be able to give you the low-down on the ones that they think are worth working for.
If there are some local firms you want to work at they may tell you which agency supplies their drivers, as not all agencies can get you in at all companies.
Hth & good luck.