Yes, it's certainly possible to do it.
In the USA, hardware stores sell spray cans of microwave oven paint and also small tubes of "touch-up" paint for the same purpose. The colours are limited to the usual beige, cream or other neutral colours that are found on the microwave cavity wall.
These paints are specifically formulated for this purpose, but I don't know if they are sold in the UK. Try searching the web.
Don't use bog-standard gloss paint whatever you do.