William was in the house Friday night for Taylor's show, with his 2 eldest children in tow ... George and Charlotte ... at least according to a report from across the pond. Royal reporter Roya Nikkhah says PW is at the London shindig with the kiddos, ringing in his born day.

Taylor's London performance happened to land on William's 42nd birthday ... so it seems like this was his big bday present. They've rubbed elbows before BTW, but that was way back in 2013.

Kate Middleton was NOT in attendance, at least that's the intel that's floating around right now ... remember, she's still battling cancer, of course, despite a recent public outing.

Anyway, while Taylor performed at Wembley Stadium, which seats 90,000 ... there incredibly hasn't been any footage of William and the kids that's surfaced (at least not yet) -- which suggests they were trying to keep a low profile, probably in a super private box somewhere.

We've got footage of another big name that's there though ... Taylor's boyfriend Travis Kelce was in the house, and he didn't shy away from the cameras whatsoever.

Joining Travis at Taylor's show ... big brother Jason and his wife, Kylie -- so it's a family affair.