Hi, welcome to the site. My name is Max and I will help you with your question.
In the insurance policy there is usually a clause that says when it would be repaired as opposed to replaced with new.
It is usually to do with market value and whether the thing being repaired is beyond economical repair.
If you can show the insurer that the thing is uneconomical to repair, by reference to the visits to repair and cost to them so far,then that should mean you become entitled to a new one.
I thought there was some legislation that continual failure makes the item not fit for purpose.
The legislation is the Sale of Goods Act 1979.
That requires the fridge-freezer to be of satisfactory quality.
There isn't anything that specifically says that an item that continuously breaks down then it must be replaced under an insurance policy.
If it keeps breaking down though, then you should be able to argue that it's not of satisfactory quality and that you're entitled to a replacement or your money back. The argument would be that it is a breach of s.14 of the Sale of Goods Act 1979.