Originally Posted by matthewuk

I think you're doing it wrong!!!

with BA you just follow flight connections and join the Domestic immigration passport control where there is rarely any queue of note. You then get your photo taken (again minimal queue) at which point you have cleared the 35 minute conformance rule. Fast track just helps a little bit in security and can be the difference (but sadly rarely is) between grabbing a bacon roll in the lounge or not. The OP doesn't even need to do immigration.

To the OP, a 60 minute connection will be fine as long as your inbound flight is on time. If it's more than 10 minutes late then you will probably miss your connection but that's to be expected (?) If you really MUST be in TLS on that flight then you need an earlier flight to LHR. You can save quite a number of minutes by running and not using the escalators. ALWAYS use lifts (elevators) in T5, they are ALWAYS faster. The only exception to this rule is the lift to T5 Galleries South.