As it's Tommy Steele and Bill Kenwright vs Lamar Fike/Joe Esposito and Marty Lacker, I know who I'd be inclined to believe.
I used to deal BJ to Mr Kenwright quite often as he liked me due to my being a big Elvis fan and knowing quite a bit about "older" music so he used to test me when he walked in. He'd walk through the main floor and shout "who's this then" if he saw me on the gaming floor. I did tell him a few times that I actually did the music at the Clermont (and even put a playlist together especially for him) but hey..............He once brought a CD in and went through the track listing trying to catch me out. I had to get a couple wrong on purpose as most of the management were standing behind him and staring at me telling me to stop as he hadn't started playing and they wanted him out as soon as possible. They banned him in the end I believe.
Tommy has said a few things that have been shown to be incorrect (a non existent Buddy Holly gig being the most well known I think) although he may well believe it and Lamar has said that it was him that flew over and met with him in London so maybe that's what he is remembering. Considering how many years it was, we all know what tricks the memory can play. Nice story though. Maybe if some photos did turn up but personally, I doubt it.
As for performing, haha, if only.