I would say that while not arranged, his family would be vetting the woman as she would need to be "socially acceptable" to the family. I'm not sure of her background, but there may not have been a lot of women that fit the bill / ran in their circles in London that didn't hear chatter about his gay life style. He may not have had a lot of options that appeased his family- or have wanted to go through all the phony courting stuff again with another woman. If he was devoting a lot of hours to his hook ups and showed no sexual interest in his dates, they'd likely figure it out.
I'm sure he was angry at the demands of his family to have a traditional life, and transferred that anger to her- even as he was duping her. You see this all the time with straight guys being angry at their wives for expecting them to fulfill their roles as good husbands and dads, even when it is what they signed up for. They murder rather than raise the kids, or have affairs and totally blame the wife. It sounds like he should have found a woman who was just in it for the payoff.