The key details:July ILO unemployment rate 4.9% vs 5.0% expectedPrior 4.9%July employment change 67k vs 67k expectedPrior 83kJuly average weekly earnings +3.9% vs +3.9% 3m/y expectedPrior +4.1%; revised to +4.2%July average weekly earnings (ex bonus) +3.5% vs +3.5% 3m/y expectedPrior +3.5%August payrolls change -26kPrior -13k; revised to -19kThe UK labour market continues to show signs of cooling, although there isn't anything here that dramatically changes the picture for the BOE ahead of their Thursday decision.The jobless rate remains unchanged from the previous quarter while the employment rate also held broadly steady at 75.1%.But perhaps the more timely payrolls number has a bit more to offer.According to the preliminary estimate, payrolled employment fell by 26,000 in August with the total now sitting at 30.2 million. Compared with a year ago, payrolls are down by 145,000.ONS is highlighting that the number of payrolled employees has generally been declining over the past two years. So, this is mainly continuing the broader trend.Besides that, wages are also cooling as well with total earnings growth slowing to 3.9% in the three months to July - the softest reading since late 2020.Putting all of that together, it points to a labour market that is gradually losing heat.Normally, softer hiring and moderating wage pressures would be welcome news for the BOE. However, the problem for the central bank right now is that the inflation story has shifted elsewhere.Higher oil and energy prices have pushed inflation risks back up the agenda, with markets increasingly pricing further BOE tightening despite signs of weaker labour demand. But for this week, markets are widely expecting the BOE to keep the bank rate unchanged at 3.75% but pressure is building for another rate hike later this year. This article was written by Justin Low at investinglive.com.