Some clarification regarding LHR tax. The item that is real expensive is the UK air passenger duty and that can approach $300. However that is not charged if you are merely connecting at LHR. That is only charged on journeys that depart UK or have stopover in UK.

If you are merely transiting LHR then you will simply pay LHR airport tax which is about $50. It is a little higher than BRU but about the same as French or German airports.

If you are booking BA then you may see huge taxes and fees but that is BA fuel surcharge. That money is going into BA's pocket not to the UK gov't.