While Edward offered to pay more, his proposed settlement was rejected. For a job of this size, the Earl will undoubtedly have had architects supervising the work who would have drawn up a detailed written specification for the builders. Quotes would have been submitted for each item. Any changes and any increase in prices would have to be agreed by both sides during the course of the work. An estimate is not binding but if a contract was signed based on a written quote, the builders would not have been entitled to increase the cost.
Specifications frequently change during the course of building work.
Speak to them and look at the work if possible. Get estimates from two or three different builders. Ask for work to be covered by an insurance backed warranty. Use a contract - the FMB has simple forms of contract for small building work. Don't pay for more than a proportion of the work in advance.