Not sure on the legalities of this, but my mum recently found herself in a mildly similar situation.
Difference is that she had had rental increases each year and the landlord was refusing to fix some major issues in the property, including a leaking skylight in her room. They requested an increase of £200 YoY from £1350 to £1550. Previous year was £150.
We weighed up options, and ultimately decided to refuse the rent increase, but to make it clear that she would continue to pay the current amount until she found a suitable property, and then give the normal amount of notice as per her contract.
She has since found and moved into a new place.
I struggle with the situation as I can see both sides. Mortgages have gone up significantly for some, so it seems fair that your rent would.
Equally, that’s the risk one takes when letting out a property. It feels unfair that the tenant takes on the responsibility of your cost of mortgage payment increases, especially if you already pay a fair bit.
I’m really lucky where I live. My landlord has been great at getting issues sorted, and my rent increases have been appropriate.