A threat to close your account might be the Bank's big stick. It is more than mere account closure because with the temination notice will come a demand fro immediate repayment of any overdraft. An entry made to the credit register as well as the porblems caused by having to open a new account, overcom the effects of your previous bank history etc.
However, it seems that a contractual term which permits arbitrary closure of your account - and also closure of your account without notice is unfair under the Unfair Terms in Consumer Consumer Contracts Regulations
There is a very readable analysis of the Regulations by John Carruthers at:-
http://www.journalonline.co.uk/article/1001153.aspx
Extract:-