If they force messengers to implement backdoors into the protocol, I doubt they will limit it to UK users. Also, conversations with UK users won’t be private anymore even if the other party is from another country.
Client-side scanning might not be enforced for other accounts but when the infrastructure is there other governments will want to use it, too.
I hope they will. My guess is that a nonprofit like Signal will pull out. They have nothing to gain and a reputation to lose. The others will probably comply by implementing some form of client-side scanning.