I would seriously consider making an effort to take less luggage. A cab to LHR at that time of day is high risk and could easily cause you to miss your connection. All it takes is an accident somewhere or even just some roadworks to slow traffic to a standstill. As has already been said, public transport is a much more reliable option. I'd suggest DLR (or cab) to Stratford then Jubilee & Bakerloo lines to Baker St to get the Paddington to get the HEX. If there are transport problems at Stratford, you have the option of taking an overground train to Liverpool St and getting the Hammersmith & City line to Paddington.

When travelling in London, it always makes sense to have a plan B in case there's a problem (which there frequently is). There's no plan B with a cab to LHR.