If you're not checking bags, and if you sit toward the front of the plane, I'm sure the 1h30m is enough time, but the 55m might be cutting it close.
Not sure your citizenship, but some countries (e.g., USA) need a visa, which you purchase on arrival (US$20) at these windows to the side of the passport control queues. So go there first before those lines build up and then clear immigration.

I just did IST-LHR this morning, and checked in only about 1h10m before the flight (and was probably one of the last!), but there was very little delay clearing outbound immigration. My arrival in IST a few days prior was around the same time as the BA arrivals, mid-afternoon (I came from CAI), and there were similarly few delays, but I got off the plane quickly and beat the crowds.

BTW, I might add that BA's Club Europe is a pathetic excuse for an international business class product on a 4 hour flight. Ugh. 34" pitch?? At least I had the fortune of sitting in an "A" seat.