I had DDs single jabs done privately with Health Choice UK, so if they are still operating I can recommend them, as hershavevworked fine - we livein the anti MMR capital & shes been exposed los & has been okay
she didn't have the Ruebella part as she'd already had that by the time jabs were due, so was apparently already immune.
My advice would be to base it on your own DCs health, if they are robust & have been fine with other jabs, then I doubt there will be any problems with MMR, lots of our friends DCs had it without problems - the one that did have problems was the least Robust of our friends twin grandsons, one twin was fine, the other not, but he always struggled with catching bugs & generally just being the sicklier twin of the 2.
My DD reacted badly to her 10 week multi jab, I wasn't told that was the reason she was very ill at the time, but reading up on the jabs at a later date, I realised that was the cause, so we stayed well clear of the MMR - & yes, bloody annoying we don't really have much choice in the UK