The reason this is happening now is that the Renters Rights Act in May means LLs can’t do no-fault evictions from them anymore. Lots of LLs are serving notice now with an intention to exit the market and sell as they don’t want to lose control of when they can end tenancy.
You need to start looking at the private rental market to see what you can afford and consider cheaper areas if needed. It’s hard, but people move all the time. Don’t rely on getting social housing.
Yes, it’s true that if you don’t vacate by the date they give you notice for, you will be able to remain until the legal process to evict you goes through. That will buy you some time but won’t prevent the move you will have to make.
It would be best to start looking for an alternative. And if you can go by the notice date, it’s best to go. Delaying should only be used if you genuinely can’t find somewhere else. But you should try. Because you will have to move. Looking at your budget and what you can afford and where you might need to move to is what’s needed. The timing isn’t ideal for you - I can see that, but affordability should be calculated in your normal salary when you return to work - assuming you have a job where that’s going to be happening.
When you rent again, LLs won’t be able to serve no fault evictions anymore. They can sell but need to give you 12 months in property before serving notice and then cannot re-let for 12 months if they don’t sell.
Your current LL may not be selling but planning to re-let at a higher market based rent, if they know you can’t afford a substantial increase. Now is the last time they can do this as otherwise they are ‘stuck’ with you unless genuinely selling.
One of the probs of having good tenants whose rents are not increased regularly, is their rents get out of kilter with market rents. Bringing them back on track with existing tenants can then be very hard as understandably it’s not popular or people can’t afford a big jump. It’s why yearly or every 2 yearly small rises are better than holding rents stable, unless you’re prepared for them to substantially drop below market levels.