A YouGov poll for The Sunday Times newspaper on Sunday said almost 50% of the voters, including many Labour supporters, wanted Blair to quit because of his handling of the war.
The poll gave the Labour party only a 30% approval rating, three points behind the Conservatives and neck-to-neck with the Liberal Democrats, the country's third main party.
It was Labour's lowest rating since 1987 when Neil Kinnock was the leader of the party and Margaret Thatcher headed a Conservative government.
A cause for greater worry for the prime minister was the growing disillusionment among Labour party activists.
A poll by The Observer newspaper found that 41% of ruling party supporters want him to stand down before the next general election, due mid-2006.
The poll suggested that 57% of Britons thought Blair to be wrong in sanctioning military action against Iraq while 81% said he exaggerated the case for war either deliberately or unintentionally.
Half the British public believe Blair should resign, according to a Mori survey for the Financial Times published on Saturday.
YouGov surveyed 2,042 adults for the Sunday Times poll. The Observer survey covered 301 Labour party members.