My guess is that they would be on either Continental or British, probably the former, because they both have nonstops to IAH from Gatwick (EGKK).
I also checked arrivals in HOU for larger business jets such as Gulfstreams. Any that looked like they were candidates (i.e. they came from some place on/near the east coast) I checked to see what the previous flights were. I didn’t find anything. I did the same thing for IAH, EFD, SGR, and LVJ and the results were no go. The search was also conduced in the “En Route/Scheduled To” section .
Then, I re-read the article. They are, with 99.9999999999% certainty, on a commercial flight (emphasis mine):
BBC correspondent Jon Brain, speaking by telephone from aboard the plane, said **the men had been seated at the back of the aircraft - before other passengers had been allowed to board **- and were surrounded by air marshals.
Of course, they could have also flown on a blocked aircraft.