I would go along the lines of reversing the questioning , politely as if you're interested,
Eg "do you work as an escort ( whatever term) from home "?
Answer puzzled " why ? would it be an issue if I were" ?
They may just answer with what you need to know like " well only if you worked from home/ violated tenancy or your son were at home/ stopping with you "
If he's not there I can't see it being an issue providing your not claiming , paying tax etc ( this would cause more problems than the current issue)
I know from 20 + years of experience in that line of work and all a parent needs to do is provide 'adequate ' childcare not good or excellent , my desk had a sign stuck on the wall next to me saying ' ' 'remember even if both parents are alcoholics this is not a reason to break up a family as long as the childcare is adequate ' this does not mean good .
Try not to panic , say it's a legal profession and ask for advice ,all kinds , what exactly concerns them ?? Turn the tables a little , don't lie but evade the truth a little " I have a couple of friends who visit etc"
If they think anyone's staying or in the house while your sons is in, their main concern would be a crb police check, but that would be the same if anyone were in your house.
Also if your son is on a care order or any form of child protection order ( usually your Mum would have that so she can sign 'guardian' forms .
This could well be their main concern as opposed to your work , ask and see , the funds are not in place to do much else about it . Play not daft but a little surprised there's an issue at all .
Social services are very very used to 'rumour' but sometimes ( usually at someone's insistence) have to follow it through.
You could also say you considered it but haven't done just dated and it put you off . I would imagine it's someone who's gossiped so they have to check out .
I've worked with families of the most atrocious crimes against children it's unbelievable , even worked with paedophile social workers ( fact) and the children stay with them as they're to scared to make a statement.