What can be withheld from the tenancy deposit

Tenancy Deposits

I use a letting agent as a find only service for my properties and they hold the tenancy deposit. A tenant has moved out and left the flat in a very poor condition and they're telling me there's hardly anything I can withhold from the tenant. The carpets are ruined but they're saying the carpets only have a lifespan of 7 years and as they were replaced in 2008 can only claim 1/7 of the cost of new carpets. These carpets were in good condition. One of the kitchen floor tiles has clearly had something dropped on it and has smashed. They're telling me it's "It is more likely that thermo movement of the sub floor could have caused the tile to crack". I can't claim for re decorating and there's other items that have been tampered with and taken but they say there's no proof. The tenant left part the way through a month and didn't pay the rent due. They're telling me I can't claim that either. Does this sound right. There seems to be no point doing an inventory at the start of a tenancy if this is right. Regards. Gordon