i'm increasingly out of touch with benefits thing, but
this may be worth a read.
sounds like DWP will try to prove that you are still a couple but there are grounds for arguing.
(from a quick read of it) sounds as though proving that you have separate addresses (getting names on some of the bills would be probably be best, although if you're living at parents' home, that may be difficult - although things like each of you registering for a GP at your new address may help) is the thing, rather than a rigid 'not allowed to stay over more than x nights a week' rule - although DWP may try to argue otherwise.
with the old housing benefits system, you couldn't claim housing benefit if you were 'renting' a room in parents' house. i'm really not sure what the rules are on UC but you may not get a housing element to it. if you'd factored this in, then you need to seek advice from someone who knows the latest rules better than i do.
also, you might want to think about whether you being there might generate costs for parents - if it's parent in the singular and they are getting single person discount on their council tax, you being there will affect that (i think you will even if you're on benefits) likewise if they are getting any means-tested benefits, again you moving in may have implications.
the other angle, giving up a council tenancy (however run down it is) is something not to do lightly, as you may have difficulty getting back in to social housing as / when you need to, and at least as an existing tenant you have (in theory at least) got the potential to seek a transfer (you say you're on maternity leave - will having another child put you in a higher priority for somewhere bigger?)
private renting can be more crappy, and you've got no security of tenancy once the first 6 months somewhere is up, then you usually have to find a deposit for a new place before you get the deposit for your current place back (assuming you don't have to put up a fight to do that) and most landlords / agents don't want to touch anyone who's on benefits.
would it be worth trying to pursue getting whatever repairs etc are needed done first? local citizens advice may be able to help (some areas there are tenants' associations and so on) or pester your local councillor/s if you've already not got far with the housing department.
not saying 'don't do anything', just adding a few things to think about first...
