I guess it depends on how you determine that. There have been several elections in which the majority was less than the number of Scottish seats won. The swing in Scotland is usually not so drastic as to affect the result much.
"Steg....Wales and Scotland were an important factor in 1997 as I recall !"
In 1997 Labour won 418 of the 659 seats available. 328 of those were in England, meaning that only two were needed from elsewhere to gain an overall majority.
I do not think that Scotland will have any effect on the overall result. The SNP are vehemently anti-Tory so any gains made by Labour at their expense will merely be changing one set of anti-Tory MPs with another.
Another thing to note is that in Scotland the Tories go by the name of the Scottish Conservative and UNIONIST party. The importance of the second adjective should not be overlooked; this is what primarily sets them at odds with the SNP.
In 1997 the Tory leader was Major. In 2001 it was Hague. I would class neither as a pillock; Major was the victim of circumstances whilst Hague is a scholar and very erudite. He has written the definitive biography of Pitt the Younger, which was received to great acclaim in academia.