Insulation around cupboard under stairs

[areyouhavingagiraffe]

Hi all, have various gaps where the various services come in. Can I cover these, am conscious we are not supposed to use anything flammable? Or do I focus on the gaps in the door and what can I use for this?
Pics of bother gaps below. Have googled and I am none the wiser

It's a good questions, we have wrapped some towels around some exposed hot water pipes, is this unsafe?

You can push some of that soft loft insulation into any gaps in the external wall and on the outside you can fill gaps with a pot of mortar from b and q or Wickes.