Do I have grounds to take this further? Incredible noise and mould in a hotel room

Chyna-s

Just a shame you did not look it up on Tripadvisor before you went; I would never ever stay at a place without checking it out online.

TBagpuss

I think the difficulties you have are that you didn't book it, so you don't have any first hand information about what was said, and it may well be that the contract was with your mother's partner, not with you.

If you had left and gone elsewhere when you found out what the room was like then you might be in a stronger position.

You didn't get a good night's sleep but you did stay, so I'm not sure that you could claim  a full refund.

A cleaner walking in is regrettable but not material, other than as an indication or poor service. 

You can leave a review on trip advisor, you can follow up your formal complaint and specifically request a partial refund.
You could try contacting the consumer  agony aunts / uncles for one of the newspapers - both the Telegraph and Guardian have money related consumer specialists and they often manage to get something out of companies for poor service - negative publicity in a national newspaper is powerful - I am sure other papers have similar services, so you might get somewhere if one of them picked your letter to address. 

I think the moral of the story is to check out a venue yourself - it was nice of your mum to arrange it but I imagine it would have been easier to cancel and book elsewhere if you'd looked it up and decided 'no thanks' as soon as she told you, rather than after you arrived.