Thanks for your question. It's not good news though.
I'm afraid that the company is correct. A statutory cooling off period is only implied in to contracts executed away from the Seller's premises under the Consumer Protection (Distance Selling) Regulations 2000:-
This is the only cooling off period implied in to consumber contracts, so if you signed at their premises and there is no cooling off period in the written contract then you will not be able to cancel unfortunately.
If the works are defective or there is some other breach of an express term of the contract then you may be entitled to a refund/damages as a result of the sale of goods/supply of services legislation or under simple contract, but as it presently stands you are contractually bound to pay the purchase price and they are contractually bound to provide the contractual service.
I am very sorry it could not be better news.
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