Thanks, it's an excellent letter and covers the law and the issues in dispute.
You could perhaps include that breaches of the Landlord and Tenant Act provisions can result in prosecution by the local council and the landlord can be fined. It is also be breach of contract on their part and you would be within your rights to terminate the tenancy agreement and sue for compensation.
The Local Authority Environmental Health Officers have powers under the Housing Act 2004. They have a duty to ensure that properties in their area are in a habitable condition, and will serve improvement notices on landlords of properties which are assessed, under the new Housing Health and Safety Rating System as having ‘category 1 hazards’.
The local authority grants a licence to the landlord on the proviso they are fit to be landlord, do not breach the contracts, and ensuring the properties are habitable. You could threaten a report to the housing department to inform them of the landlord's conduct.
Also it would be a fast track case, not small claim - a small claim has a limit to £10,000. A fast track case is £10,000 to £25,000, making it slightly more complicated - feel free to come back to this site for ongoing guidance if you need it. The landlord may refuse the claim and you may have to issue court proceedings so if you do, let me know - I can offer the guidance.