Getting into a relationship with a British woman who has an adult child is not much of a Plan B at all, for those thinking along those lines. In the event that his asylum claim is refused and he wanted to rely on the marriage / unmarried partnership (and they're not in that type of relationship yet in any event) then they would would have to show that there were "insurmountable obstacles" to the relationship continuing in his home country. Her not speaking the local language, not knowing anyone, being separated from family, not being likely to get a job - none of that is considered to be 'insurmountable obstacles.' A woman who already has minor children from a previous relationship (if they are in contact with their father) would be a Plan B, because there would be insurmountable obstacles to her leaving the children behind and / or to taking them and thereby ceasing contact with their father.
Plan C would be to leave the UK and apply for entry clearance as a spouse / unmarried partner, but decision makers will often apply Part 9 of the Rules alleging that a failed asylum claim constitutes an attempt to contrive to frustrate the intention of the Rules. Which then leads to a lengthy and difficult (and expensive) appeal process.
I'm not oblivious to the issue of people finding a handy girlfriend in the UK and pledging undying love to the prospect of a future visa, but a woman with an adult child would be a terrible option.
Also, asylum claims are taking YEARS to determine at the moment. It's natural for people to get on with their lives - joining hobby clubs and getting work (once they've been waiting for a year they can apply for permission to work in shortage occupations) and forming relationships. I wouldn't assume that someone in this position is cynically contriving a sham relationship.
It sounds to me like the major issue OP has is whether her family would be sniffy about it - and they might be, but that's rarely a determining factor in relationships.