In law you're renting from the landlord not the estate agent. The agent is literally that, an agent for the landlord.
By law, an address in the UK for the landlord has to be made available to you within, I think without looking it up, 14 days of your written request. Without a valid UK address for the landlord you don't have to pay rent - although I wouldn't actually advise not paying, but the law says you don't have to. If you did withhold rent you would need to pay it back once the address was forthcoming.
You could possibly find out the name and address of the landlord by visiting the Land Registry website. It costs less than �5 I think.
If the property was uninhabitable while work was being carried out then the landlord is responsible for finding you alternative accommodation. Also, you can't be expected to pay rent whilst not being able to live there.
In your position I would write to the Agent telling them that you intend to pay a proportion of the rent for the month i.e. if you couldn't live there for 3 weeks then you only pay 25% of the rent for that month.
I have to ask the question though, if there was so much wrong with this property, why did you ever move in?