London elections set to leave British PM May down, but not out

* May's Conservatives bracing for losses in London vote

* Setback unlikely to topple May but could fuel Brexit dissent

* High hopes of Labour Party gains may prove hard to achieve

By William James

LONDON, April 29 (Reuters) - Voters in London are expected to punish Prime Minister Theresa May's Conservative Party at local government elections this week which could embolden critics of her Brexit strategy, but are not expected to trigger her downfall.

London and some other regions will on Thursday elect the local officials in charge of day-to-day public spending - a vote as much about issues like refuse collection and road repairs as it is about the national debate on immigration and May's plan to take Britain out of the European Union after a 2016 referendum.

The elections are seen as a bellwether of public sentiment and polls show voters are ready to deliver a critical verdict on both May's leadership and her party's eight years spent pursuing a policy of public spending cuts to shore up Britain's finances.

"A government that's been in power for eight years with an austerity programme is naturally going to suffer at elections," said Robert Hayward, a former Conservative lawmaker who now sits in parliament's upper house and specialises in polling analysis.

A YouGov survey published on April 26 gave the opposition Labour Party, led by Jeremy Corbyn, a 22 percentage point lead over the Conservatives in London, putting it on course for its best performance in the capital for 40 years.

Thursday's vote will come less than a year after a snap parliamentary election splintered the previously rock-solid foundations of May’s position, stripping her party of its majority in a vote she had expected to win easily.

The result of that general election has been a weakened leadership, open dissent among Conservative lawmakers over exiting the EU and a nagging fear for some investors that her government could fall and be replaced by socialist-led Labour.

Thursday will not directly affect May's practical ability to govern: the vote does not cause seats in parliament to change hands and the slim working majority she has thanks to a deal with a smaller party will be unaffected.

But a below-par performance will embolden critics in her party and could then complicate the already-difficult task of executing her Brexit plan without making concessions to pro-EU factions, such as agreeing to stay in the EU customs union.

"Politicians always look at the last set of election results and by definition they're going to look at what happens on May 3 and make a judgement on that," Hayward said.