THE clearest evidence yet of a slowdown in the service sector, which has been spearheading the recent rapid growth of the British economy, emerged yesterday as the nine-strong monetary policy committee gathered at the Bank of England for its two-day meeting to decide interest rate policy.

The City expects the Bank to signal at noon today that it has left base rates unchanged on 7.25% for the seventh month in succession. With the manufacturing sector in recession and services coming off the boil the economy seems set for a period of below-trend growth.

This has led most independent economists to conclude that rates have peaked, but with headline inflation at 4% and the underlying rate at 3% it is likely to be some time before the Bank risks reducing them.

The service sector continued to expand in May, according to the latest survey from the Chartered Institute of Purchasing and Supply, but at the weakest rate so far recorded.

The strong pound undermined competitiveness in the sector last month, but buoyant domestic demand kept new business coming in.

An overnight forecast from a US think-tank that sterling was overvalued by 25% against the German mark and would fall to DM2.30 in the medium term caused the pound to retreat to around DM2.90, but UK economists thought the report from the Washington-based Institute for International Economics went too far.

''We wouldn't go as low as DM2.30, but DM2.60 to DM2.70 is a pretty sustainable range,'' said Jonathan Loynes. UK economist at HSBC Securities.

''The fundamentals should help the pound down towards these levels, and the interest rate differential with Continental Europe will narrow.''

One of the biggest fears of those on the Bank committee who favour a tight monetary stance is a sharp fall in sterling, leading to further inflation.

The institute's business activity index for the service sector, first published in July 1996, dropped for the third month in a row to a seasonally adjusted 56.9 from 59.1 in April.

One persistent fly in the ointment is the threat of wage inflation.

Skill shortages and higher wages were again cited by purchasing managers as a problem in the service sector, particularly in computing.

The business expectations index fell from 75.9 in April to 74.4, its lowest reading since the survey began.