You are absolutely right dzug. Apologies all, I took a brainstorm there. I was getting myself confused with the fact that tax free interest stops on date of death (on any account, not just an ISA).
I imagine you are correct and that's what the bank clerk meant. I just looked up the rules on savings accounts and ISA's on the Halifax website and there's no suggestion on there of interest stopping. In fact it says this:
"25. What happens if you die?
If you die, and your account is not a joint
account, your personal representative can use
the account (even if the number of the account
changes), and close the account without losing
any interest for �early closure� (see condition
18.1). If your account is a joint account, see
condition 16.5."