We were in a similar position to you a few months ago op. we have a joint income of £36000 so a bit less, but our mortgage is less than your rent (about £400 pm though that could go up if interest rates rise).
We were in debit every month - dh ended most months between £700 and £1000 overdrawn and I was a couple of hundred overdrawn too.
We took stock of finances and spending in January and realised we were spending loads on coffees, meals out etc and also not planning weekly supermarket shops effectively. I was popping to tesco most days!
All we did initially was to meal plan and cut down to eating out once a fortnight but to cheap places using clubcard vouchers. This alone saved us a fortune and we started to claw back the deficit.
Then dh looked at all our bills and found cheaper alternatives for many of them. We have never had sky, just free view.
Now we are both used to the new way of living and I kid you not - in 6 months of budgeting and tracking spends we will now end this month both in credit by a couple if hundred! Not long until we can start saving regularly! I never would have thought this possible before. And we do not feel deprived at all. Still have nice food - I cook something nice at home on our Saturdays in (eating out was our main luxury) and I quite enjoy my weekly shop planning and list making! It might all go to pot soon as I'm facing a large pay cut :( but I am confident we'll still be ok.
My point is, it can be done - just a look at all spending and analyse everything and you'll be surprised. Start small if it seems too daunting - start with looking at one thing, food/meal planning, or clothes, or bills - and see what you can save there, then move on to the next thing.
Good luck!