G-BBAE
Nice thought, but there is little chance of you getting bumped into First.
Also, it tends to be full of boring old farts and you definitely wouldn't like the atmosphere, which is very quiet, usually with the window blinds down, 'cos the FTQVs like to sleep enroute.
More likely that you would get World Traveller Plus or maybe Club, if you were very lucky.
However, WT+ is very nice and Club is excellent, so you might get lucky.
On the other hand, if you read your ticket terms and conditions, you will find that this sort of compensation is offered as a goodwill gesture, not a right.
And if you do find yourself offered a deal to travel via LHR, I'd suggest that you talk nicely to the agent, since BA has quite a "soft" culture and responds well to reasonable pax - you want the agent on your side, not agin you.