Hi
That sounds very tight - especially security and passport control can be a bit messy (long delays happened to me at the entrance of the B/C Gates). Also worth to mention that luggage check in for BA is now in Terminal A and you need to walk to B/C (rather strange I know - not sure if that has changed again but I doubt it). Your flight might depart from B but security/ passport control is sometimes closed there and you need to go via C.
You might have a problem at security if - happened to me a few times - if there is an Emirates and/ or Qatar flight departing the same time with you at C (fast track will be pointless as you have too many business travellers). Hint: There is now an additional security lane (upstairs!) at Terminal C (just go up the escalators) which is a bit of a secret and normally quite empty. From there you can walk over to the B terminal if required (about 5min with a separate passport control airside).
I would strongly recommend to rebook so you can visit the excellent Airbraeu Wirtshaus (a local restaurant) brewing its own beer/ weissbeer which is very good and EUR2,70 for 0,5 litres (as a Bavarian I know what I am talking about, I am stopping there before every flight to London
You'll find it between T1 and T2.