Help needed to recover damage to the property

I had a tenant on shorthold tenancy with details as below

Tenancy from June 2007- Dec 2011.
I hold the tenancy deposit worth £1500.

Damages in my estimate - £4000 (I had deployed an independent agency to repair the damages)
e.g. some of the damage is below
Carpet reinstalled due to stains etc - £1500(it was newly installed during tenancy)
Kitchen hob -stains / burns - installed new - £200
Windows etc never cleaned throughout the house - cleaning expenses - £500
Wallpaper scraped / damaged (7 years) - £500
Kitchen platform - scrape - £200
Damage caused by condensation to walls etc.

I have had a long email chain with the ex tenant and they are disputing these claims.

Unfortunately no inventory was done at the beginning of the tenancy. Also at the end the inventory was not done. I arranged for an independent inventory to be done in March 2012 (property vacated in Dec 2011) - the property was vacant for 2 months since I was busy and the damage.

Also I have the bills for carpet and hob that were newly installed during tenancy.

Now the tenant has always disputed the claim. I tried sending notices through the lawyers etc but no effect. I still hold the deposit however the damages are more than the deposit amount and I need to recover. (PS: I did not hold the deposit in the TDS scheme).

When I make the claim the tenant always says
- this was the state of the property at the beginning of tenancy
- they also ask for return of deposit and some advance rent that was paid to me
- they ask for TDS certificate for the deposit
- condensation was caused by the exhausts not working (but I think they just did not bother to keep the windows open) They are also saying this caused them health issues.

We are still talking and exchanging emails. But I am getting frustrated.

Is my only option now to go the court?