Who is responsible for repairs?
You are responsible for repairing all damage you cause, and for minor repairs like changing lightbulbs, tap washers or bleeding radiators. If you cause damage, you are responsible for the cost, even if it falls under the landlords responsibilities below.
Your landlord is responsible for repairs to the structure of the building, including windows, doors and guttering. He is also has a responsibility to maintain any existing supply of water to the property together with sinks, baths & WCs.
Your landlord is also responsible for maintaining all water heating, room heating, gas appliances and the supply of gas and electricity where applicable. That does not mean that the landlord has to provide these things if they don't exist.
All other repairs would be subject to the terms of your tenancy agreement.
What if my landlord won't do repairs?
The important thing to remember is that you can NOT withold rent because repairs have not been done. You may be able to seek damages through the small claims court for the landlords breach of contract, but you should take legal advice on that.
The environmental health officer at your local council may be able to offer help and advice, including liaison with your landlord. In extreme cases, they can organise repairs without the landlords cooperation.
Shelter have some very good advice on how to get repairs done by a reluctant landlord at http://england.shelter.org.uk/get_advice/repairs_and_bad_conditions/repairs_in_private_lets/tenants_doing_repairs