LONDON, Oct 24 (Reuters) - The pound edged up against the euro on Tuesday, shaking off data that showed the UK labour market lost more steam in August and business activity deteriorated this month as an economic survey for the euro zone was even worse.

Britain's unemployment rate held steady at 4.2% under a new calculation that accounts for dwindling survey responses from households, while the number of employed people fell by 82,000 and the number unemployed rose by 74,000.

Sterling was last up 0.24% against the euro at 86.90 pence and flat against the dollar at $1.2247.

A separate survey showed Britain's businesses reported another decline in activity this month and cost pressures have cooled further, underlining the risk of recession ahead of the Bank of England's interest rate decision next week.

The "flash" preliminary reading of the S&P Global UK Purchasing Managers' Index (PMI) for the services sector fell in October to 49.2 from 49.3 in September, the lowest reading since January and below the 50 no-change mark for a third month.

A Reuters poll of economists had pointed to an unchanged reading.

A PMI for the euro zone was worse, showing business activity in the bloc took a surprise turn for the worse this month.

Money markets show traders believe UK rates have now peaked at 5.25% and could realistically start to decline by around June.

Just three months ago, traders were preparing for a peak of 5.8% by May 2024 and the prospect of the first decline by September.

Since then, inflation has declined to 6.7%, from 7.9%, while growth has struggled to show any year-on-year increase.

"It’s hard to believe that sticky inflation and higher interest rates won’t have more impact on the surprisingly robust economy. Focus is now all on the upcoming round of central bank policy decisions," Neil Birrell, chief investment officer at Premier Miton, said in a note.

(Reporting by Amanda Cooper; Editing by Susan Fenton)