British politics will undergo a “significant realignment” after the EU referendum which could see the Liberal Democrats follow the example of their Canadian cousins to mount a serious challenge to be the main party of government within the next decade, the party leader, Tim Farron, has said.

As he hailed the “quiet rise” of the Lib Dems after their devastating losses in last year’s general election when they won only eight seats, Farron said his party could become a major force at the 2025 general election as a “meeting place” for pro-EU liberals from Labour and the Conservative parties after the referendum.

Farron said the presence of pro-EU Tories and Labour MPs appalled by the “utter shambles” of Jeremy Corbyn’s leadership meant the Lib Dems could entertain ambitions higher than simply holding the balance of power within a decade.

In a Guardian interview before this weekend’s spring conference in York, the Lib Dem leader said he hoped to repeat the success of the new Canadian prime minister, Justin Trudeau, who took his party from third place in 2011 to lead a majority government last year.

“I know all the analogies to the Canadian Liberals don’t stack up entirely,” he says. “But they were not seriously thought of as the alternative government to the Conservatives certainly even 12 months ago. You have just got to push your chest out and when an opportunity arises, fill that space, so we need to do that … The scale of the task is massive but I don’t see why my ambition shouldn’t be equally massive.”

The Lib Dem leader, whose party shrank from 57 MPs at the 2010 general election to just eight MPs last May, said the party was enjoying a “quiet rise”. Adrian Sanders, who lost the Torbay seat last year to the Tories after 18 years in parliament, stormed back in a local council byelection win last November. The party has also seen its vote increase in council byelections this week in Farron’s Westmorland and Lonsdale seat and in Theresa May’s Maidenhead constituency.

Farron, who declined the opportunity to serve as a minister in the coalition government and carved out a niche as a grassroots campaigner to the left of Nick Clegg, secured a decisive win in the leadership contest last year. But the Lib Dem leader has had to fight hard to establish his presence in parliament in the past year after the Lib Dems lost their cherished status as the third party. Farron is only allowed one pop at prime minister’s questions every three months, which he has used to highlight what he regards as the main parties’ timidity over the refugee crisis.

In his Guardian interview Farron moved to set out distinctive yellow water between the Lib Dems and the other two main GB parties with a strong attack on the investigatory powers bill, or snooper’s charter, published by the home secretary earlier this month. The Lib Dem leader warns that far from helping combat terrorism the government’s proposals will undermine the fight because the powers handed to the intelligence agencies are too broad.

“There are always finite resources in terms of time and attention as well as money, but every hour spent on looking at what people are shopping for on Amazon is time not spent tracking people who are a genuine threat to our security,” he said. “If you are looking for a needle in a haystack, don’t triple the size of the haystack. We hope the bill will be gutted and will come back as a proportionate and effective response to the terrorist threat … It undermines our ability to catch people who are a genuine threat to our country because we will be permitting the security forces, services, to look at data that in reality is of little interest.”

Farron hopes that his strong stance on touchstone liberal issues such as the snooper’s charter shows that the Lib Dems could provide a welcome refuge for like-minded Labour and Tory politicians who may feel alienated by their parties after the referendum. “It’s frustrating that a classroom squabble between Boris and Cameron is becoming the focus of this referendum and potentially runs the risk of us losing it,” he said.

The Lib Dem leader recalls how the 1975 referendum on Britain’s EEC membership failed to resolve differences over Europe in spite of the emphatic yes vote. The winning side within the Labour party, led by Roy Jenkins, founded the breakaway SDP six years later when the losing side, led by Tony Benn, sought to move the party to the left.

Farron believes that even if the remain side wins in this year’s referendum, many pro-EU Labour and Tory MPs may feel more comfortable with the Lib Dems as he embarks on his “two-election strategy” (2020 and 2025) to return his party to the frontline.

“The question is whether this is a historic moment where we could become the meeting place for liberals in other parties and there could be some quite significant realignment around the Liberal Democrats. I don’t want to say things which are not deemed credible at this moment but we could have ambitions higher than that [holding the balance of power in a hung parliament].

“I’m not going to get my crystal ball out but I am quite sure there are good liberals in both of the other parties and there is one Liberal party which is united and very comfortable with being liberal. The point is, how do we get ourselves into a position where we are sufficiently credible and have sufficient mass to be that Liberal party? Who knows? A hundred years ago there were two progressive parties. One blew the moment, one took the moment. Who knows?”