I spent a week there in June 1986 trying to get good photographs of the sea-bird chicks etc. at Bempton, and at Flamborough Head. The main problem photographically is that the coastal cliffs face north-east at Bempton, and also stick out into the sea to a degree, so much of the upper cliff face is in shadow after quite early morning. Whether this is also true at sea level I don't know. (Flamborough Head may be better as parts stick out more and may catch the mid morning sun better. In the afternoon the sun is behind the cliffs.)
I did get to the top of Bempton Cliffs one morning around dawn, and was rewarded by a snow squall.
So fast lenses with image stabilisation would clearly help, as your boat is never going to be that stable. I'd recommend at least a 200mm lens, and be prepared to raise the ISO level if you're using digital. Watch your metering as the cliff rock (apart from the guano) is quite dark, and you really want to retain some detail in the whitish/very white plumage of most of the birds. I'll be very envious if you get a shot of a gannet diving for fish!
Good luck - I was using film & a slow 300mm f4.5 lens in the days when Kodachrome 64 was clearly sharper than any of the 400 ASA offerings.