The council will NOT lend them a deposit willy nilly.
He has to fulfill certain criteria which, I very much doubt he will after being here only 2 weeks.
Any deposit is paid straight to the landlord, not the tenant and it is a fixed amount depending on the council's LHA (Local Housing Allowance) for a 1 bed flat. They will not fund a flat deposit elsewhere.
Your son, IF he passed the criteria, would have to tell the landlord he was receiving housing and unemployment benefit as the landlord would need to give the applicant their name ( as ut appears on the bank card, bank sort code and account number and also the address of the property and landlords telephone number as the council usually ring up to confirm details.
You usually have to be in dire straits AND receiving benefits to be allowed to apply and, as your son is living with you, he isn't in dire straits or yet receiving benefits.
It is a small finite fund which is administered cautiously to only the more deserving cases.
I know this as I have been instrumental in dealing with these problems in my voluntary work with homeless charities.
Your son's partner cannot work until she has applied for and granted a work visa which is finite and must be renewed otherwise she would face deportation.
Have you ever thought that this was the plan all along? Free health care, better pay and 'granny' to cushion the realities of life.
Some of your OP doesn't make sense.
You say that your son 'messed up his degree' to be with her (translator)
Was he taking the degree in Asia and left the course, or was he taking the degree here and left to be with her in Asia which begs the question, how did he he get to know her?
Personally, I think you've made a rod for your own back.
You don't say how old your son is, or what jobs he has previously had or if he's ever worked at all.
Frankly, it sounds a right mix and I wouldn't be surprised if it all came tumbling down around your ears.
Son sounds as if he'd quash your ability to see your grandson if you didn't meet his requests and that's not good.
All I can say is...good luck.