One bookmaker has even started paying out on a victory for Mark Reckless, the former Tory MP whose defection to Ukip triggered the contest in the north Kent constituency.
So do poverty analysts and critics of the former Commons Speaker, Michael Martin, whose enforced resignation triggered the contest in this traditional Labour stronghold.
Smith, whose entry into the race for party leader threatens to derail the hopes of Angela Eagle, who first triggered the contest, said it was clear people wanted both access to the single market and controls on immigration.
Mark Reckless - the former Conservative backbench MP whose defection to the Euro-sceptic party triggered the contest - is enjoying a 12 percent lead over the Tories at 44 percent, while Tory candidate Kelly Tolhurst is set to gain 32 percent of the vote.
He said Labour's candidate, 28-year-old PR consultant Naushabah Khan, would focus on concerns about immigration and the NHS as she fights against her "two Tory" opponents – the Conservative candidate who was named as local councillor Kelly Tolhurst and the seat's former Tory MP, Mark Reckless, whose defection to Ukip triggered the contest.
Mr Reckless, whose defection from the Tories to UKIP triggered the contest in Kent, travelled to London soon after his election to take his seat in Parliament, saying his constituents expected him "to get back to work".
The electorate's shock decision to vote to leave on 23 June triggered the leadership contest, after Cameron, who had campaigned strongly for a remain vote, said he would step down to allow a new prime minister to guide the complex negotiations.
The contest, triggered by the death of the previous MP in June, will be on the same day as a by-election in Sedgefield, Tony Blair's former constituency, which also needs a replacement as Mr Blair heads off as a super-envoy to the Middle East.
Turnout was just over 50% in the contest, triggered by MP Mark Reckless's defection from the Conservatives to UKIP.
