Suella Braverman’s “dream” of flying refugees to Rwanda could be realised by the end of the year and before the next election, government sources have said.

The home secretary believes that “with a fair wind” the European court of human rights in Strasburg could rule on the controversial policy by the end of 2023 and is unlikely to overturn UK court rulings.

Government sources said that even if there is a referral to the supreme court, Braverman’s team say that a deportation flight to the east African country may well take off before the next general election.

It comes as Downing Street declined to rule out that the UK could withdraw from the European convention on human rights if it was seen as necessary to stop small boat crossings, despite serious misgivings among some Conservative MPs.

Rishi Sunak last month said that “tackling small boats” was his top priority in government – a risky move given Boris Johnson and Theresa May failed to employ policies which reduced the numbers.

Braverman spoke in October of her zeal in getting the Rwanda deal across the line. “I would love to have a front page of the Telegraph with a plane taking off to Rwanda, that’s my dream, it’s my obsession,” she said.

Judges in December ruled that the policy, which is intended to stem the numbers of people crossing the Channel from northern France in small boats, was lawful.

In January, the same judges allowed part of their ruling to be challenged in the court of appeal.

Sunak’s official spokesperson has stressed that No 10 was confident a promised new bill to try to limit the number of refugees and migrants arriving unofficially would comply with international treaties, but refused to say what could happen if the European court opposed the plans.

However, other officials said that even if withdrawal from the ECHR was considered, it would not happen in this parliament. If eventually seen as needed, it would most likely first be included as a manifesto pledge for the next election.

Any move to leave the ECHR would be deeply controversial, in part because its provisions form part of the Good Friday peace agreement, but also because it would leave the UK with Russia and Belarus as the only European countries outside the continent’s joint rights framework.

Asked about a report in the Sunday Times that Sunak planned such a move, the PM’s spokesperson said only that a bill due in the coming weeks to tackle the small boat crossings would comply with the ECHR, and refused to be drawn on what would happen if it did not.

“I don’t get into sort of unsourced speculation on future plans,” he said. “All I can say is that policy approach of the government when it comes to tackling this issue will both deal with the underlying causes and seek to be compliant with our international obligations, including the ECHR.”

While a number of Conservative MPs would support withdrawing, citing local worries about the number of people arriving in the UK unofficially, such a plan would be vehemently opposed by others in the party.

Leaked messages last week in a Tory MP WhatsApp group showed some “red wall” MPs complaining that they would never be able to enact the policy of deporting refugees to Rwanda if they did not leave the ECHR, while others warned of a backlash.

One Conservative MP told the Guardian they would be very surprised if Sunak made such a move, and that they suspected talk of withdrawal was being led by Suella Braverman, the home secretary, who has previously called the small boats “an invasion on our southern coast”.

“Some colleagues in red wall seats would absolutely love this, and even in my seat it might go down well,” the MP said. “But there would be massive kick-back from colleagues in the more Lib Dem-facing seats in the south.

“If the PM does do this, it will create a big division in the party. And if he doesn’t, it won’t. So I don’t personally think Rishi wants that fight. I think this is more Suella flying a flag.”

According to the Sunday Times, Sunak is prepared to quit the ECHR if the Strasbourg court rules against the bill.

The proposed new bill, cited by Sunak as one of his five key policy promises, could prove problematic under ECHR provisions given it is widely expected to state that would-be refugees who arrive in the UK outside official channels will not even be allowed to claim asylum.

The bill, which is now not expected to be published until after next week’s February Commons recess, could also remove the right of appeal against deportation, or permit it only after the deportation has happened.