I know that some companies such as Jalite will make vinyl or plastic inserts for illuminated fire exit boxes so that you can replace the signage without having to replace the whole box, but I can't seem to find anywhere that sells plastic or vinyl inserts that have the version of the running man signage with the flames behind it like this:

Is there anywhere willing to do this such as Jalite if I ask, or would I need to get an emergency bulkhead light like the one below an stick signage like that above onto it?

Jactone will make to order, their ex stock overlays are only ISO ones. It's been decades since I've seen NHS Estates symbol overlays sold ex stock, might be easier to use a standard non illuminated sign with a EL fitting no more than 2m away.

Why do you need an illuminated exit sign assuming it is not a place of public entertainment, I see many that are just not required and it would be easier to use a standard exit sign with a EL fitting no more than 2m away?

I need such a sign for a lecture theatre and a drama/dance studio at a college.

Point taken, you do need an illuminated exit signs so why not fit illuminated exit boxes with BS 5499 standard templates.

If it's not a hospital there is no need to use the elusive NHS Estates Symbol and just get the more readily available ISO 7010 pictogram, loads of maintained exit boxes with this pictogram available (but check as some suppliers are still trying to offload fittings with the discredited EC pictogram)