I'm afraid that I have am inbuilt mistrust in the system and would never trust getting a connection in one hour with morning arrivals at Heathrow. Personally I would have flown to Paris and gone on one of the many flights to get me to Toulouse to ensure that I got the train,or got the train from Paris.
I would be astounded if BA paid out for a €450 taxi = good grief where on earth where you going that it would cost that much?
I do wholeheartedly agree about those trains however - I think that 2min is wishful thinking. It always seems longer to me. Whilst we are about it why can that elevator outside Harrods not be the up escalator when you have to squeeze between a huge Decaux poster and the entry to Harrods to get to the lift downstairs. That wretched Terminal is full of bottlenecks. Until every flight comes into a gate with an airbridge and the Third World of A10 and the other is a thing of the past I do not consider T5 to be anywhere close to being a World Class anything.