I have never been cheated on in my marriage, so please don't assume everyone on this thread is projecting their own hurt.
Snap. Have a lovely faithful dh of 20yrs. OP, why do you think that most, if not all the posts on here are unanimous? Read the relationship threads, look at the lies the wives have uncovered, as told by their husbands. Pretty similar to what your boyfriend is telling you. Making excuses for not getting divorced etc. Showing you just enough that you think all is OK so don't feel the need to 'snoop'.
They all follow the same pattern, you are not stupid, but you are massively naive. There is a reason that you & he aren't 'out there' 'public' and that is because you are his secret. Yes, show him this thread, it will be interesting to hear what he has to say.
To answer your question, surely of he is separated, he already knows what a 'gold digger' of a ex he has & doesn't need you telling him. But in reality, by telling him, he will know that his lies are convincing you & will happy with himself.
Also, if they are separated and he has teens, why don't they visit him in London at the weekends now & then? He doesn't have to go home, does he?
Does he stay at the marital home at weekends? Because if his teens are old enough to be exposed to the wives boyfriend during he week, but know that dad still stays at weekends, they are probably pretty much older teens, therefore, they would accept you, hands down!
The truth is, that you ARE the ow. The wife seemingly has no worried with the kids meeting her boyfriend, so why should the husband care?
Lies, op. All lies. Please wake up to him before he leaves you high & dry, possibly pregnant.