Generally speaking an estimate does not amount to an offer and is not legally binding, although if the final price is significantly higher than the estimate you can claim a breach of the statutory ‘reasonable cost’ term. You should be clear about getting a quote rather than en estimate, as this will then become the final price as agreed as per contract. However if it turns out that more work is needed as required by law or regulations (e.g. a fire escape to be installed , or adjustments made due to building control requirements), the supplier will be able to recover these additional costs from you. If however, they are outrageous, you can legitimately argue they could and should have been reasonably foreseen by the supplier, and bring a case for misrepresentation.

How can I resolve the situation?

What about contracts for services?