Thank you for your helpYea it's the 'plastic wood effect' over chip board...
If it were me, I'd give it a good clean off with fairy liquid (to de grease it). Mask off any vents and glass with masking tape and news paper, and buy yourself a couple of 'plasti-kote' aerosol spray cans. You can usually get it at The Range, Wilko's etc.
Apply a fine base coat first, leave it to dry for an hour and then apply a second and third coat with 1 hour dry times inbetween.
Needless to say, your tort doesn't want to be anywhere near his enclosure wile the paint is applied or is drying just to be on the safe side.
You could of course try finding multi surface paint and hand paint it but the finish will never be as sharp as a spray can and will take much longer to paint and dry.
Depends how deep into it you want to go I suppose.