You should be fine. A few years ago, I did an MR where I landed into London Stansted (back when AA flew there) and flew out of LHR. Due to delays, I only had four hours to transit. I cleared immigration, took the coach across town, cleared the dreaded LHR security, and even had time to lounge hop in all that time.
By the way, the UK immigration officer marked me as in-transit, presumably between the US and US.