English country houses varied a lot in size and technology and the era they were built in. The cost and number of workers who built them no doubt greatly varied.
Legend claims that William Beckford was so eager and impatient while building his legendary Fonthill Abbey that he employed hundreds of workmen and had them work in shifts around the clock with hundreds of torches for light at night. Yet it took 17 years from 1796 to 1813 to build.
Beckford's 500 labourers worked in day and night shifts. He bribed 450 more from the building of the new royal apartments at Windsor Castle by increasing an ale ration to speed things up.
Mark Girouard in The Victorian Country House 1979, Introduction, section 8 "The Building of a Country House", page 17, says about Westonbirt: "When building was at its height nearly 300 men were on the payroll. At Bear Wood, in June 1868, no less than 380 men sat down for a banquet given by the owner, John Walter of The Times, to celebrate the roofing-in of the house."
Westonbirt House is described on pages 424 to 425 and was built from 1863 to 1870. Bear Wood is described in chapter 20, pages 263-272 and was built from 1865 to 1874.
These examples show that even when a large country house took years to slowly build there were sometimes hundreds of workers employed at one time.