* No clear front-runner in race to succeed Boris Johnson
* Ex-finance minister Sunak won first two lawmaker votes
* Sunak and foreign minister Truss clash over tax
* Outsider Tugendhat viewed as best performer by public (Recasts after debate)
By Michael Holden and David Milliken
LONDON, July 15 (Reuters) - British foreign minister Liz Truss clashed over tax policy with former finance minister Rishi Sunak on Friday, as the five remaining contenders to be Britain's next prime minister went head-to-head in the first of three televised debates.
An initial field of 11 challengers has been whittled down following two days of votes by lawmakers from the ruling Conservative Party. But no individual has yet emerged as the obvious successor to Boris Johnson who announced he was stepping down following a series of scandals.
While Sunak has topped those two votes, he faces stiff competition from Truss, who has the backing of a number of senior figures, and junior trade minister Penny Mordaunt, who polls suggest is the most popular with party members who will decide the winner.
Former equalities minister Kemi Badenoch and Tom Tugendhat, chair of parliament's Foreign Affairs Committee, also remain in the running but trail the others in support from Conservative lawmakers.
A snap poll by market research company Opinium of the British public -- who do not get a say in the Conservative Party decision on the next prime minister -- showed Tugendhat was viewed as the best performer by 36% of viewers.
Sunak came second on 24%, followed by Mordaunt and Badenoch on 12% and Truss at the rear on 7%.
Whoever gets the job will take on rocketing inflation and low economic growth, as well as the public's lack of confidence in politics after Johnson's scandal-ridden time in power.
Sunak and Truss tussled over economic policy in the debate, hosted by broadcaster Channel 4.
Truss has proposed scrapping increases in payroll tax and corporation tax proposed by Sunak, at a cost of over 30 billion pounds ($36 billion) a year, to be funded by a slower reduction in government debt built up during the COVID-19 pandemic.
"We have to be honest, borrowing your way out of inflation isn't a plan, it's a fairy tale," Sunak told Truss.
Truss said tax rises would undermine business investment just as the economy was faltering.
"You cannot tax your way to grace," she said.
Voter polls also suggest the Conservatives are falling significantly behind the opposition Labour Party.
"I'm very aware that while my party chooses a new leader, you are watching us pick your next prime minister... I hope you like at least one of us," Mordaunt told television viewers.