Get a cat

Cats love warm radiators to sleep next to so they will naturally be near the mouse problem

Maybe CC is free

Once it’s eaten a couple, naturally leaving the head on your pillow, they will soon get the message and go somewhere else

Or a mouse trap bated with peanut butter (far better than cheese)

I'm not fond of mice or other vermin or pests.

In fact, I'm allergic to animal hairs and the presence of mice actually triggers my asthma. So the mice can't stay and neither can a cat. There used to be a cat roaming around our garden when we last had a mouse problem and I've not seen it around for a while.

I'm thinking of metal collars or sleeves to go around the pipe to take up as much space as possible and polyfilla the rest.

Do you reckon the mice bumped the cat off?

Sorry, but late on this, but you can get heat resistant expanding foam - here.

Pack coarse steel wool (brillo pad is too fine really) into the hole and seal it up with foam, then trim it back when it sets. Or use grab adhesive - Gripfill, Pinkgrip, whatever - as well as steel wool. Coarse steel wool is fine as a mouse-deterrent, just remember they can get through a gap as small as the end of a pencil...

If your boiler is reasonably modern, it'll have a display that shows the "flow temperature"; they can get quite hot - mine's showing 70°right now with a room temp of less than 20°.

HTH, Pete