Grant's Warriors are currently lying in second place in the RaboDirect PRO12 standings, but struggled in Europe, registering their first win in the competition against the Saints.
And Grant, who has five Scotland caps, is convinced that he and his Glasgow team-mates can take confidence from their victory into international duty.
"The Glasgow boys have gone into the Scotland camp on a real high, with confidence and self-belief really strong right now," Grant told the Glasgow Evening Times.
"There had been a lot of frustration that after five matches of the Heineken Cup campaign we had nothing to show for our efforts.
"We knew that was simply unacceptable and we also knew that we had to get the win to restore some pride.
"But I think the manner in which we got that win was huge and we have to make sure that our enthusiasm and confidence is infectious throughout the Scotland squad.
"I don't see any reason why we can't face England with anything but high hopes - the great thing is there are 19 Glasgow boys in the squad and a good few former Warriors and that is a plus.
"With the training camp having been in Scotstoun this week it has almost been like a continuation of the Glasgow set-up, so it has been great."
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