LONDON, July 13 (Reuters) - Former finance minister Rishi Sunak won the biggest backing from Conservative lawmakers on Wednesday (Jul 13) in the first vote to choose who will succeed Boris Johnson as party leader and British prime minister, while two more rivals were eliminated.

Sunak, whose resignation as finance minister last week helped precipitate Johnson's fall, secured support from 88 of the party's 358 Members of Parliament (MPs), with junior trade minister Penny Mordaunt second with 67 votes and foreign minister Liz Truss third with 50.

Nadhim Zahawi, who took over as finance minister from Sunak last week, and former foreign minister Jeremy Hunt were knocked out after failing to get the required minimum of 30 votes. They join three other contenders who dropped out the day before.

Those remaining - which also includes former equalities minister Kemi Badenoch, Attorney General Suella Braverman, Tom Tugendhat, chair of parliament's Foreign Affairs Committee - will go through to a second round on Thursday.

Subsequent ballots will be held among the Conservative lawmakers, eliminating the candidate with the fewest votes each time, to whittle the field down to a final two by Jul 21. The new leader will then be chosen from those two by the 200,000 Conservative party members in the country at large, and be announced on Sep 5.

While Sunak might be the most popular contender with his colleagues, a YouGov poll of nearly 900 party members found Mordaunt was the favourite, beating any of the others in a run-off. She had a huge lead over Sunak, who fared badly against almost all his rivals, and is now the bookmakers' favourite.