As the commercial catering market is not very innovative (everyone sells the same variations on a theme), look on the various suppliers websites (Nisbets would be a good starting point) and see what pixies its second cousin feeds on.
Showing a photo of the whole thing is useless. Take a picture of the cable - the conductor cross section area will tell you a lot as it is against regulations to put more than 1.5mm^2 into a standard plug. If there is a cover on the machine where the cable enters, take that off and make a picture there.
FWIW, I think that style of appliance is called a 'salamander grill'. I've never eaten grilled lizard myself, but hey ho.
13 amp plug will take 3 kw on a grill they have a few plugged in where i do work in a shop and caffe they get warm as there on 5 hours a day . they tend to burn the pins and socket after about a year ive altered 3 of em and put them on seperate 16 amp supplys as they were overloading the ring main