I asked Bio, who's busy doing a genetics degree, and she checked it out and said that...
...it turns out that the p in p53 stands for 'protein' and that the protein is coded for by the gene TP53. So if you just saw p53 written down, it's referring to the protein. But generally, if you were to come across some similar looking code type thingys (for example: saxA+, npfK1, fusA2 etc.) then I'd always assume it was a gene unless it said otherwise.
I guess there's always a possiblity that medical texts would use a different convention to biology texts, so it might be worth checking with your tutor, especially before you start writing essays.