Can I suggest one more thing? Can you put a free add on Gumtree for it? Or a local FB page. Maybe give it a week or so and then do what you have to do. I know it's unfair that responsibility has been placed on you but the cat didn't ask for this situation, either. There may be someone out there who is willing to rescue it if you post an honest ad describing what's happened.
I've rescued 3 cats, one of which appeared at my backdoor carrying it's tiny kitten in it's mouth! It had given birth in the shrubs in my garden and I ended up re homing all of them within days of advertising them to good homes on Gumtree. I realise it's a PITA to do, but just a thought before it's left to the elements.
Good luck! Poor kitty 😞