Right, they have British citizenship, so the bit about them "wanting to stay in the UK" isn't really an issue - they have the right to be here, and I'm guessing have British passports (They would be crazy if they haven't............all the places you can visit with one etc).
The next point, well it covers a number of points, those being
She doesn't know you are together yet
They have stayed together because of the children
He will not get a divorce because he's Catholic.
Well, they are in the UK now and divorce is allowed. Granted the church won't recognise it as proper divorce, but I can tell you if you went to a local Catholic church and asked (extremely discreetly obviously), you'd probably find loads there were divorced. Not re-married in the church obviously, but still divorced. They're a lot more open than people think, ultimately it's up to people's conscience with their God.........if you believe in that of course, and if you don't, then it's no big deal is it
Divorce is not expensive in the grand scheme of things, IF both parties are both in agreement. Not the thread to be discussing that side though.
What is worrying me a bit is the rest. She doesn't know. Oh they are only staying together because of the kids, oh I'll leave her eventually, oh I can't leave her because she would be devastated, but I'm living in a hellish relationship, honest. I'm sorry but the world is full of women who are just the "bit on the side" who swallow this story year in year out. In reality they are happily married, having sex like rabbits, but he's just greedy and selfish and wants to have his cake and eat it.
Now I'm not saying yours fits this description, but this seems to be more common than not. Do be careful there.
The last bit about would she take the kids away..........well yes of course she could, and probably would - in that she would almost certainly get custody of them. In fact, in an "acting like adults and sitting down talking about it" sort of divorce, this they would agree between themselves, and it is a fact that in most cases, women are a bit better at taking care of kids than men. It's biological and cultural. Not in all cases obviously - I'm sure we all know cases of some feckless bag who has no idea, but anyway.
What is near certain (If this is maybe your worry - or perhaps the story he's giving you) is that she's highly unlikely to take the kids and leave for the Philippines. Why on earth would she do that when she wants to remain here, she has a British citizenship, and therefore would be eligible for a raft of benefits.
A mother living on her own will almost certainly be better off then when she was married, unless he had a highly paid job. This is especially so if she is working 16 hours or more.
Is she going to leave all this and go off to somewhere with not much money? As if!
Lastly, I'm certainly not giving lectures about breaking up marriages, no way. It takes two to do that, he has chosen to meet you, so it's not you. You just want the best for yourself - and him.
I am on your side, and not giving lectures about that. I am just frankly worried this is yet another married man using you for his own little fun, and has no intention of treating you right.