A survey in East Renfrewshire found the former cabinet minister remains three points behind the Nationalists, but that is six closer than the last similar poll in March.
Mr Murphy’s fightback appeared largely down to Tories, with nearly a quarter of those who voted Conservative in 2010 now saying they would vote for him on 7 May.
Lord Ashcroft’s final round of polling in marginal seats produced mixed results.
The Tories completely reversed a four-point Labour lead in Croydon Central and Conservative employment minister Esther McVey closed the gap with Labour in her defence of Wirral West but Labour were on course to overturn a 4,861 majority to take Peterborough.
“Taken together, the results show that there can be late movement on the battleground as the election approaches and there is still room for more in the final week,” Lord Ashcroft said. “That is why even these polls remain snapshots, not predictions.”
Labour were boosted by a five-point jump in their overall rating to 34 per cent in a Survation poll, putting them just back ahead of the Conservatives, unchanged on 33 per cent. Ukip shed two points at 16 per cent, the Liberal Democrats were down one on 9 per cent and the Greens dropped one to 3 per cent.
Lord Ashcroft’s East Renfrewshire poll had the SNP ahead by 39 per cent to Labour’s 36 per cent, with the Tories – who held the seat comfortably prior to Mr Murphy taking it in Labour’s 1997 landslide – on 20 per cent.