I made the exact same trip UA to LHR & BA to Lisbon last summer. We arrived early morning at Heathrow - walked 15 mins from the UA gate to the inter-terminal shuttle, waited another 15 mins for the shuttle, waited 30 mins to get through security, and another 15 mins for BA ticket counter. I would say to allow yourself 2 hours to be safe. You do not have to clear passport control or customs at Heathrow.