Opposition candidates gleefully accused Mr Godfrey of "throwing in the towel" after he was filmed by a BBC television crew telling a disgruntled voter: "I don't mind which way you vote as long as you don't vote SNP."
Mr Godfrey, set to lose the seat to the Scottish nationalists by up to 7,000 votes, denied that his comments amounted to an admission of defeat. The by-election was a "head to head race" between Unionist parties and SNP "separatists" and defending the Union was his main concern, he said.
"There are people I have met who want to register a protest vote to make their view clear to the Government. That's fine. That's democracy. What I am saying is, register your protest but do not give support for smashing up the UK."
Opposition parties ridiculed his comments. Roseanna Cunningham, the SNP candidate, accused the Tories of panicking. "I cannot understand how any politician could go on to a doorstep with that line. Mr Godfrey has exposed the anti-Scottish nature of the Tories' campaign," she said.
For Labour, Douglas Alexander, who is in second place in opinion polls, said: "This is desperate stuff - a crude attempt to make this by-election a constitutional showdown."
Veronica Linklater, the Liberal Democrats' candidate, said she felt sorry for Mr Godfrey. "He has acknowledged he is out of it. Ah, pat him on his little head," she said. Archy Kirkwood, her campaign manager, added: "I'm not sure whether an endorsement from John Godfrey is a blessing or a curse. This is the first time in 20 years that I have known a by- election candidate approve other parties."
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