How to chase back the outstanding rent from tenants?

Did the male tenant serve notice to end the tenancy? If he did and if the tenancy was ‘periodic’ then the tenancy ends for both parties. If it was in its fixed term then the male tenant remains joint and severally responsible for all of the rent.

I’d speak with the remaining tenant to ascertain her plans. Can she afford the rent on her own? Do you want to take her on as your new tenant with a new AST agreement?

Personally, I’d employ an eviction specialist to deal with it. Section 8 if two months in arrears. Section 8 if the tenancy has ended (periodic and one party gave notice) and Section 21 for efficiency.

I'd settle for getting the tenant out - right off the rent. Not worth your stress and mental health.
then sell.
but getting a court date and then Bailiffs - can you sell with tenant in situ to some new landlord who has no idea of the s..t storm he is taking on? Difficult if declare the arrears.
do you have rent guarantee on it?
do you have tenant guarantee?
If no to both
- best of luck - you will need it.

You've got more going on here than worrying about back rent. The moment the tenant informed you he was no longer residing in the property should have been the point you spoke to the remaining tenant and possibly served notice to vacate as technically AST terms breached. Very difficult circumstance to navigate especially with young children involved but you are not a charity or social worker. Highly probable this will get much worse in terms of no rent and you have good reason to evict based on that point alone.

Putting your capital into the PRS is risky and it’s going to get riskier and the nett returns are not so attractive nowadays compared to other investments especially if you borrowed money and cashing in your investment when you need the money is not quick or simple. It sounds harsh, but this tenant is costing £1200 a month so needs to go. Most landlords are just glad to get their property back after the eviction process. Attempts to recover arrears are mostly doomed to failure. A CCJ does not help if the ex-tenant does not have the wherewithal to pay. Right now Section 21 would appear to be the safest bet but you could be nearly £10,000 down by the end of the process depending on how it goes.
Serving notice might force the situation. We recently served a Section 21 because for family reasons a jointly owned property has to be sold (not the best tenant but no arrears). The tenant went to the Council and the Council got in touch with us basically asking under what conditions were we prepared to keep the tenant on (none in this case). Maybe this would happen here. Maybe some sort of deal could be done as paying the rent would be cheaper for the Council than providing temporary accommodation, lots of maybes but you never know. Maybe our tenant will just leave when notice is up, maybe they won’t and we are in for the long haul, maybe they will just leave while the eviction process is ongoing, maybe they will get free legal representation, maybe they will pay the rent to the end, once again lots of maybes, who knows at this point?

If the Council are paying part of her rent, then does that mean the tenancy or his liability somehow ended?

Going to court and bailiffs can take forever and cost and at the end of it you’ll be very lucky to get any back rent - I’ve been there! My tactic now - is sending a text saying you’ll be calling round to do the usual flat checks next time you’re in the area but don’t quite know when! The tenant is then on edge - not knowing when there’ll be a knock on the door! . Just hope you’re phone number’s not blocked. I’ve only used this method once and it worked!

1st off the Tenancy agreement doesn't expire, it can only be ended by the Tenant giving Notice or a Judge. (It will likely be now on a Periodic or rolling Tenancy)

Issue a Section 21 ASAP.

The male has been a bit stupid in blocking you, as he is still liable for the rent - jointly & severally with the female (I'm presuming AST was in both names?)

You may be better in incentivising the female to leave. Also advise her to take the Section 21 to the council to try & get re-housed, although be aware they will prob advise her to stay put until you have gone through Court process.

Hindsight is a marvellous thing!

Why did you not purchase a Rent Guarantee Product to start with and let the Rent Insurer obtain possession and, of course, continue to pay the rent!

You mention the husband has a good job.

did you know a ccj can be detrimental to the tenants good career. If he is in a very good job, or in that type of business, you could push him to resolve it by doing an online small claim.

eg insurance, finance, directorships, high level jobs and f100 business, high public profile business, often assess the risk an employee poses eg a ccj could be living beyond means =:potential to steal money

as well as doing above advice

Ring the guy from a different number. Demand the rent.