Uber has a great number of options for different car types and prices. UberXL is a fairly new offering so I'm not sure how many drivers they've signed up for that, but I rarely have difficulty finding an UberLUX or UberX (the cheap option) vehicle.

Although you'll be better off in the larger UberXL or UberLUX options, it's worth pointing out how cheap UberX is. For example to Central London from any of the LHR terminals is £37, south of the river (Hilton Rotherhithe) is £40. Door to door and cheaper than the HEX for two passengers!

I use Uber when I'm not in a particular hurry to get to/from the airport as it's much more relaxing than a train or the tube (but when short of time, using the train is usually more predictable timewise). I normally use Hailo for shorter taxi journeys within Central London just so I can get a proper cab that can use bus lanes.