Advice needed on tenant rights

So yesterday I signed a Assured Shorthold Tenancy Agreement with a local letting agent for a property. At the point of signing they stated that the Gas Safety Check had been carried out that morning and that everything had passed except the gas fire in the living room, this isn't a major problem for me as the property has Gas Central Heating throughout.

On arriving at my new property I noticed the following issues:

1. The front door has dropped and there is about a 1/2 inch gap on the one edge of the door meaning cold air is leaking in. When I viewed property letting agent let me in so I didn't notice this.
2. Hot water tap in kitchen is defective meaning I have no hot water to clean in kitchen.
3. Several radiators do not work. I checked for air locks, opened thermostatic valves but again they do not work.
4. The electric shower is leaking internally in the plastic housing, I could clearly see water leaking out and could hear electrical arcing.

So bearing in mind I only signed the agreement one day ago what recourse do I have? Can I request cancellation of agreement on the basis the house is not fit for purpose and the electrical shower is unsafe? I have emailed Letting Agents to inform them of these issues but am a little unsure of what rights I have....

Any advice would be appreciated....