The firm's chief economist Chris Williamson said growth in the sector remained strong, "although the pace of expansion slowed."
"We must remember that growth was exceptionally strong in previous months, and also that parts of the country saw record rainfall in January," Williamson said.
The purchasing managers index in the service sector for Britain posted a level of 58.3 in January, the lowest mark in seven months and a drop from the 58.8 reading in December.
The index uses 50 as a break-even point. Above 50 indicates growth, while below 50 indicates contraction.
Despite slower growth, "companies reported being able to conduct business in a conducive economic environment, with considerable success in converting inquiries into hard contract wins," Markit said.
"With business optimism about the future reaching the highest for almost four years, we should see growth revive again in February, hopefully as the weather improves and households and businesses
dry out from January's rainfall," Williamson said.