Oh dear. I can really sypathise with you.
Our DS2 got a 2.2 (top uni) & was looking for a grad job for a whole year, duiring which time DH and I were worried sick.
My advice to myself in those bad times was to try not to worry/criticise, and let him deal with it. It's his life.
At least your DS has a partner to help him/talk things through which is a comfort? Also, with a 2.2 in maths, he must be quite clever! So there must be a (good) job out there for him somewhere ... especially as he had 19 months of work experience before he hit this 'barren' patch?
He just has to work out what he wants to do, & what sort of job suits his personality & ambition. And then find a way to get a "in". Manchester is a reasonably good place for getting a job I would have thought? (And experiencing job growth?)
Of course, your DS might need to review his options/direction occasionally, (with a view to trying a different approach), in case he's really flogging a dead horse on the track he's on. But as someone (sort of) said earlier, it's very unlikely he will NEVER ever get a good job again. (It would be so wasteful to the UK economy to have maths grads long-term in min wage jobs?)
If it helps, there are a LOT of young people in same boat as he is at the moment. (Their parents just don't shout about it on FB.)
Can he get any relevant unpaid work which would help his profile? (Has he considered tutoring in IT/maths?)
Anyway, just hang in there as his mum. Give him general advice, (if you have any), but mainly just send him your love & support. Tell him it will all turn out fine if he keeps going/applies for lots of stuff.
I like the phrase "God helps those who help themselves". (Tho I am an atheist!) Cos the harder you try, in general, the luckier you get?
Best of luck to him and you!