I'd go with the Alternative Dispute Resolution within the Tenancy Deposit Scheme framework. I've heard that they are VERY strict with landlords and rarely approve deductions from the deposit. Seems to me that you've got nothing to lose by just telling the landlord that we'll see what comes out of the dispute resolution.
If you are lucky, you'll find they never put your deposit in a scheme at all and they have to pay you 3 times your deposit.
In England. And, was there a check-in inventory when you took the tenancy? And if there was, did you sign it and were given your copy? The check-in inventory is what the landlord has to compare with against the check out inventory. No check-in inventory then there is anything to compare with for any deposit reductions and therefore deposit returned in full.
The government's tenant guide states not to sign the check-in inventory if it is not correct. The landlord had to give you a copy of this guide.
The law also states that the deposit is for any damage and that fair wear and tear cannot be deducted. The landlord cannot have betterment. Nor do you pay for the damage the landlord/ landlord's cleaner did when the used the wrong product or the wrong cleaning sponge for the surface: the landlord has admitted their cleaner did that damage.
The landlord also had to tell you which Deposit Scheme they used for your deposit.You should have had an email from the Deposit Scheme they used, giving you your reference.
You can search for where your deposit was held
https://www.gov.uk/tenancy-deposit-protection/if-your-landlord-doesnt-protect-your-depositI hope you put in your dispute with the Deposit Scheme as jimbocz suggested?. In not, do this asap so they know there is a dispute. You don't want the landlord being given your deposit by default; otherwise you would need to take them to court to get your money back: it happens the other way around too. It’s very easy to raise a dispute. Don't waste time emailing the landlord or the letting agent if you don't agree with what they have said and have told them this: this is where the Deposit Scheme resolution comes in for the tenant.
When a dispute is put in, the landlords’ who lose get a black mark put against their name and if they have done this before, it can get to the point where they are never allowed to take a deposit again. Landlord must know the laws of their business, but tenant is not expected to know those laws.
If their letting agent fails to respond to the dispute that the deposit scheme then raises with them, you are given your money back. It does happen as it is the landlords who are liable for all the laws they must follow. Letting Agents don't need any qualifications or training: they don't even need a DBS check!
Not held in a Deposit Scheme is slightly different to what
@jimbocz has said: the deposit must be returned in full and
up to 3 times the deposit must be given to the tenant. At one time the government had to close a loophole when that badly written law meant that rolling over to a periodic tenancy, meant that it was 3 times back and then another 3 times back for every month until the tenant moved out.
If your deposit was not protected, it is now too late for the landlord as their tenant has moved out. Landlord will likey want to settle out of court with the full deposit back, plus they must pay at least 1 times the deposit back and it could be 3 times; that court will decide. As the law used to say it must be 3 times, it is likely those landlords who don't follow the law changes, will still think it is 3 times: don't tell them the law changed as there is a good chance their letting agent will not know either.