"I'm not sure about the UK, but in the US the term "CheckBook" is a very generic one meaning the small register used to record a person's checking account. "
Not to sound like a broken record, but whether a term is "generic" depends on how it is used.
"Checkbook" for a check register would be generic.
It would certainly make a dandy registrable trademark for a brand of deodorant, if someone had the inclination to sell deodorant under the name "checkbook".
So, in this HYPOTHETICAL, if "checkbook" were a brand of deodorant, and you registered the domain name with the intent to re-direct visitors to buy some other brand of deodorant, then, yes, you would have a trademark problem.