* UK services PMI picks up slightly faster than expected
* News follows slumps in manufacturing and construction PMIs
* IHS Markit says Brexit, global trade tensions, hurting business
* Composite PMI remains near weakest since 2012 (Adds reaction, wraps in car sales data)
By David Milliken
LONDON, June 5 (Reuters) - British economic growth almost ground to a halt last month, as modest expansion among services firms barely offset weakness in manufacturing and construction caused by the Brexit crisis and weaker global growth, a business survey showed on Wednesday.
The IHS Markit/CIPS services Purchasing Managers' Index (PMI) edged up to 51.0 from 50.4 in April, its strongest reading in three months and slightly above economists' average forecast in a Reuters poll.
Equivalent surveys for manufacturing and construction published earlier this week unexpectedly fell deep into contractionary territory, and taken together the three PMIs gave one of their weakest readings since 2012.
"The PMI surveys collectively indicated that the UK economy remained close to stagnation midway through the second quarter," IHS Markit economist Chris Williamson said.
A euro zone PMI was only slightly stronger, as businesses across Europe face challenges from the trade conflict between the United States and China as well as Brexit.
Official data showed Britain's economy grew a robust 0.5% in the first quarter of the year, though much of that was driven by firms stockpiling ahead of a Brexit deadline of March 29, which has since been postponed until Oct. 31.
The Bank of England forecasts Britain's quarterly economic growth rate will slow to 0.2% for the three months to June.
There was no reaction to the data in financial markets. Investors think the BoE is more likely to cut rates than raise them over the coming year, despite it saying it expects borrowing costs to rise gradually if a Brexit deal can be done.
"Overall this points to positive but weak second-quarter growth, and a Monetary Policy Committee on hold until Brexit is resolved," said Morgan Stanley economist Jacob Nell, who does not expect rates to rise until August 2020.
The PMI surveys do not cover the retail sector, which benefited from strong consumer demand in the first quarter. More recent signs have been less promising, though.
Car dealers reported a 4.6% annual fall in sales for May earlier on Wednesday, and the British Retail Consortium said its members - mostly high-street chains - suffered a 2.7% drop in sales, the biggest fall in more than 20 years.