Adam Tomkins told the BBC that the party had reached its “ceiling” in Scotland in its current form and needed to change if it was to ever gain power.
The former MSP for Glasgow retired from the Scottish Parliament ahead of last May’s election, but has been a long-term proponent of his party splitting from its UK counterpart.
The warnings came as Boris Johnson continues to ride out the ongoing scandals around Downing Street parties during lockdown.
Tory MPs and cabinet ministers have repeatedly poured cold water on the prospect of the Prime Minister resigning, arguing instead for disgruntled backbenchers to wait for a report into the gatherings by civil servant Sue Gray, potentially due to report later this week.
Douglas Ross, the leader of the Scottish Conservatives and MP, called for Mr Johnson’s resignation on Wednesday after the Prime Minister admitted attending a party on May 20, 2020.
All 31 Scottish Conservative MSPs are understood to have backed the move, however Mr Ross faced criticism from cabinet ministers including being described as a “lightweight” politician by Jacob Rees-Mogg.
Speaking on the BBC’s Sunday Show, Prof Tomkins said a split from the UK party could be an element of the necessary consequence of Boris Johnson staying Prime Minister after the calls from the Scottish party for him to resign.
He said the Scottish Conservative brand, as part of the UK party, was no longer credible, stating a new “robust vehicle” for centre-right politics in Scotland was needed.
Told Mr Ross could not go into a general election asking for people’s votes while Boris Johnson leads the UK Tory party, Prof Tomkins agreed and said something would have to be done.
He said: “I think that’s right. If you’re a Scottish Conservative person and you call in public for the resignation of the leader of the UK Conservative party and that resignation does not come, then you’ve got a choice to make.
"You could prove your critics inside the party, Jacob Rees-Mogg, right by doing nothing about it.
"Or you could say, well there needs to be consequences for this and the time has now, it has long since come, that those of us who are on the centre-right of politics in Scotland, need a credible and robust vehicle through which we can bring the policy ideas that we have got about economic recovery, about social policy, and indeed also about the constitution although I wouldn’t put that front and centre.
“My view has been for some time that the Conservative Party is not the appropriate vehicle.”
He added that such a split “follows” from Mr Ross’ statements during the week, stating that the 31 Conservative MSPs in Holyrood will have to “think really hard” about the relationship, “if any”, with the UK party should Mr Johnson stay as Prime Minister.
Prof Tomkins added this question is a “real and live question” in Scottish politics regardless of who leads the UK Tory party, but that it had been “crystallised” by the calls for Mr Johnson’s resignation.
The former MSP accepted that opinion among backbenchers in the Scottish Conservative party might disagree with him on the future, but argued that the party in its current state will never win power.
He said: “Ask yourself this question, if not now, when?
“It seems to me as if the Scottish Conservative party has reached its ceiling in Scotland at the moment.
"We are doing much better than we were 10 years ago thanks to the leadership of people like Ruth Davidson and Douglas Ross, we’re at 25 per cent of the vote rather than 15 per cent of the vote and that is significant progress over the course of the decade.
"But for me it is not enough. I don’t want to see a centre-right force in Scotland stuck at one quarter of the seats in Holyrood and one quarter of electoral support, I am more ambitious than that for centre-right politics in Scotland.
"It seems to me that we’ve now reached the point where we can't go any further and that’s under the current structure that we have.”
He also rejected the suggestion that Douglas Ross should resign if Boris Johnson stays as Prime Minister.
Prof Tomkins said: "Douglas has stood up for what he believes in, Douglas has proved he is a man of steel.
"If that becomes a resignation issue in Scottish politics then we are all doomed.
Polling expert Sir John Curtice, who also spoke to the BBC’s Sunday Show, said any split from the UK party would not solve the Scottish Conservative’s short-term problems.
Asked whether a new party could succeed, he said: “The truth is that we don’t really have any data on this.
“What we do have is a long running debate, it goes all the way back to the leadership battle between Ruth Davidson and Murdo Fraser back in 2011.
"I think what one can say is that kind of project of persuading people you’ve created a new party with a different image that is more separate from Westminster is a long-term project.
"It is not something that is likely to solve the party’s immediate problems because you’ve really got to persuade voters you are something different and that doesn’t happen in a matter of weeks and certainly not between now and the beginning of May.”
A Scottish Conservative spokesperson added: “The Scottish Conservative and Unionist Party are fully focused on Scotland’s recovery from Covid and holding the SNP to account.
“We won 100,000 more votes than ever before in last year’s election and were the only pro-UK party to move forward.
"In this year’s local elections, we will be standing candidates right across Scotland with the aim of removing the SNP from power.”