Mark Diffley said Conservative infighting could also provide a boost to Scottish Labour.
Tensions erupted earlier this week after Scottish Tory leader Douglas Ross called on Boris Johnson to resign following the Prime Minister's admission that he attended a gathering in the Downing Street garden during lockdown in May 2020.
Mr Diffley, the former director of Ipsos MORI Scotland, said the situation was potentially "a gift" to Scottish Labour and its leader, Anas Sarwar.
The Scottish Tories have been seen as the party that "puts up the most robust and united defence of the UK", he said, but the public may feel that no longer holds.
He said: "That's the risk that [Mr Ross] has, and actually that may give Anas and Scottish Labour an opportunity to step into that void.
"If you're a Scottish Tory voter and you're disillusioned with the UK Government, and I think there will be a lot of that about, then what do you do, and what does the party in Scotland do to keep hold of that vote?”
He continued: "There are lots of dangers here, I think, for both the party in Scotland and for the unionist, pro-union campaign in any future referendum.
"I suspect once the dust settles on this and we get some polling in Scotland, there's every chance support for independence will have ticked up again a bit."
Mr Diffley said Covid "receding a little bit" and the "visceral troubles that the Tory Party is having here and in London" could offer Nicola Sturgeon the opportunity to "try and strike while the iron's hot".
He said: "I think we need to see a bit of polling before being sure about that."
The First Minister told the SNP’s annual conference last year the campaign for Scottish independence would resume "in earnest" this spring.
Mr Diffley said: "If this runs on, if there are more stories that come out on rule-breaking, this is absolute gold for the SNP, I would think."
He added: "If Covid is starting to sort of recede into the distance, particularly as we get into the spring and the weather warms up and we get past this most recent wave and so forth, and the restrictions are lifted, that becomes less of an issue.
"And if that's then combined with an ongoing political storm, I think particularly if Johnson survives some of this, but is really badly wounded, then those two things together – if you were in the Yes movement, or pro-independence movement, or the SNP or whatever, you would be looking at that and thinking, maybe this is the time now to, what’s the first step, introduce the [referendum] bill to Holyrood, and at least begin making your move, so to speak.
"You would think that this would be politically one of the moments to do it."
He continued: "From a purely political point of view, with a Prime Minister so weak and vulnerable, you would think, everything else being equal, this would be the moment in which to try and get your agenda off the ground."