Landlord keeping my deposit

[Redadmiralflyer]

I gave my landlord over a months notice and said we were leaving on 30th Sept. We got our keys earlier than expected and have already moved into our bought house. Told the landlord this. The rent is covered until middle of October so she has an empty house for two to three weeks which we thought would allow her to decorate as she wanted.
She said to us today during the inspection she isn't happy because we didn't give her enough notice. If we had told her we were moving out sooner she could have got the place decorated and a new tenant lined up. We explained this wasn't possible as we didn't know when we were getting the keys but the rent paid is covered until middle of October. She wanted to charge us for her losing rent while she didn't have a tenant.

The place was spotless as I cleaned to a high standard. She wanted to get a cleaner in for the carpet which was 90 quid. Fair enough.
When I moved in my dd stained the cream fabric couch. I got a new couch and told her she could keep it when I left. She refused at the time and said she wouldn't charge us as we decorated the living room and put in a new carpet. Today during the inspection she changed her mind and said we should have left her the couch.
We accidently broke the light in the living room and replaced it. She was angry because we didn't keep the broken glass and didn't give her the broken light. She said it needs replacing. I did replace it with a modern light but she's not happy.
The carpet that needs cleaned has a stain and she said she would have to get a new carpet if it can't be removed. I said I wasn't going to pay for a new carpet as I put the carpet that was originally there when I moved in up the loft. She told me she wanted to use it for loft insulation even though it's been rolled up in the loft for seven years.
She called me argumentative when I raised my points with her. I actually feel fuming and surprised I didn't go through her.
Aibu to think she is trying to keep my deposit so she can cover the rent lost due to no current tenant. We gave her the legal amount of notice and paid in full for the month to cover it. She thinks if we told her months earlier she could have got a new tenant in and decorated. It's not our problem is it?

Thank you so much for the advice. Will look into all. Have had a look on the sites and I have def not been given a reference number or any paperwork so can't log on to check.
Interesting about carpets needing replaced after seven years. She told me she has had carpets far longer and kept in good condition. The carpet is light cream and my dd is now seven so had it from when she was a baby. Cream carpet in a small child's room is just a no no. However there is a dark green carpet which is clean in the loft to fit the bedroom but she isn't interested.

I am really hurt about the couch though. She had told me she wasn't charging us because we decorated and put in a new carpet in living room. She didn't want our brown leather couch so we took it with us and now she is complaining we didn't leave her a couch. She got all muddled and flustered when I challenged her because she knew she had said all this. She just wants our money. If I had known she wanted to charge for the couch I would have gave her it there and then!