The City of London has two international airports that I use frequently... Heathrow, and Gatwick. My office is very near Gatwick*, but I can get a non-stop from Houston only going to Heathrow. What to do for ground transport?
National Express runs a coach service between the two airports, with frequent departures (every few MINUTES), it's about an hour run. It's not cheap, it's 25 Pounds if you get a ticket at the last minute. Big beautiful clean coaches, seatbelts, nice.
Maybe METRO could approach Southwest and United and get them to fund a frequent IAH-to-HOU (Hobby) service, with the argument being that this will help each of them compete against the other, by making it easier for each of the to skim passengers off of the other's network and onto their own.
* My office is on the Gatwick grounds... I walk 8 minutes from the South terminal and walk into our lobby. It's very odd, but very convenient. The hotel is across the parking lot.