I have £6k in two abbey national postal ISAs. The rate is just under 5% - which is not great in current terms. Is it possible to move the money to a different ISA at a different company ithout losing the tax relief?

yes, you just need to transfer it - don't close them. Apply at new place, say you have an old ISA and want it moving accross. Most banks will accept money from other ISAs and it should be quite painless, in fact they'll probably bite your hand off...

Does it matter if you've already used this years allowance?

No, this is just a transfer and does not take up any of your allowance; unless you add to it of course.

I had to fill in a form to declare which tax years money I wanted pulled over, including the current tax year.

I was just going to ask this question myself but found this thread.

I have 3K in a lloydsTSB ISA - which is pretty pony by current standards, about 4.5% interest. I had a look into NS&I ISA but they say that you cannot transfer money from other ISA accounts.

Does anyone know of a good ISA account that will allow you to transfer?

Have a look in Moneywise or on moneysupermarket.com.