Recovering lost income from property management

Hi guys
Due to the property managers carelessness/negligence my property was vacant for 3 weeks. Last tenant gave notice way before, but the house was not put up for inspection till they left. They left earlier than the date they said they would leave and it was not relayed on to me till i called. Further to this they messed up availability date , had inspections which were not shown on internet site etc etc.

I asked for them to waive the letting fee for their negligence but they came back with commission for one week waived which is downright embarrassing. I could easily get rid of them and go to someone else.

Do i have grounds for getting money back if i went to department of fair trading or even a lawyer ?

Also they deducted letting fee once the new tenant paid holding deposit. Don’t they have to wait till first rent is paid or tenant signs the lease ?

Thanks