LONDON (Reuters) - British house prices fell last month for the first time since May as a boom in activity late last year started to lose steam, mortgage lender Halifax said on Friday, echoing similar data from rival Nationwide earlier this week. Halifax, part of Lloyds Banking Group, said house prices dropped 0.3% on the month in January after holding steady in December, a weaker performance than the average 0.3% increase expected by economists in a Reuters poll. Compared with a year earlier, house prices in January were 5.4% higher, slowing from 6.0% growth in December and the smallest annual increase since August. “There are some early signs that the upturn in the housing market could be running out of steam,” Halifax managing director Russell Galley said. Halifax reported the biggest annual rise in house prices since 2016 in November, as a temporary exemption on purchase taxes for property costing up to 500,000 pounds fuelled demand at a time when other parts of the economy were still reeling from the coronavirus pandemic. This tax break expires on March 31, and Halifax said property sales agreed now were unlikely to complete soon enough to benefit. Nationwide also gave similar reasoning on Tuesday when it too reported a monthly fall in house prices, the first on its measure since June.