Speaking to journalists at the SNP Spring conference in Aberdeen today, the former first minister said the Scottish Parliament vote next week requesting that powers be transferred to Holyrood to allow it to hold a new plebiscite would put considerable pressure on the Prime Minister to give way.
May said on Thursday she would not consent to an independence referendum in the timeframe put forward by Nicola Sturgeon, between Autumn 2018 and Spring 2019, as it would interfere with the Brexit negotiations.
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The First Minister wants the referendum to take place during this period as it would allow voters to be informed of the terms of the Brexit deal, due to be agreed by then by the UK Government and the remaining 27 Eu countries.
Allowing the vote to happen before the UK leaves could enable links to be maintained between an independent Scotland and the EU, possibly protecting membership of the new state in the bloc.
"What I believe will happen is that the UK Government will have no choice but to agree to an independence referendum and that the next referendum will deliver a Yes vote," Salmond said.
"Nicola is taking the matter to the Scottish Parliament, that is the next step, and if the Scottish Parliament backs the First Minister that impresses that clearly that is the sovereign will of the Scottish people.
"No UK Prime Minister since before Margaret Thatcher has said openly that they would stand against the sovereign wishes. In fact, even Margaret Thatcher said she would accept it. So Theresa May would be moving into a position more extreme than Margaret Thatcher.
"I don't think that position would hold for any length of time. I'm not saying it would collapse as quickly as the budget last week but nonetheless it is a position which will collapse over a period of time."
There was further support for Sturgeon's referendum plan from Health Secretary Shona Robison who insisted Scots have the right to choose independence as an alternative to Brexit. Robison warned quitting the European Union would threaten the future of the NHS.
A hard Brexit, taking the UK out of the single market, would put the future of Europeans working in the NHS in doubt, and would mean "greater Tory cuts" to Scotland's budget, Robison told delegate.
She called on her English counterpart Jeremy Hunt and Prime Minister May to "get on with the day job" instead of "pursuing their hard-right Brexit agenda".
While SNP ministers have been accused of ignoring day-to-day issues such as health and education as a result of their "obsession" with independence, Robison levelled the same charge against the Tories at Westminster.
She stressed the key role EU workers play in the NHS, with European citizens accounting for one in 20 doctors.
She said that one medic, who had spent more than 25 years working for the health service in Scotland, had been left feeling he "was no more than a pawn in Theresa May's Brexit game".
Robison said: "Scotland must have the opportunity to protect these European nationals - our friends, neighbours and families - and have the ability to attract their successors in years to come.
"Let's send a clear message today to the staff in our NHS and care services from EU countries, and those from other parts of the UK and further afield - Scotland is your home and we will do everything we can to ensure your future.
"Frankly, rather than pursuing their hard-right Brexit agenda, it's time that Theresa May and Jeremy Hunt got on with the day job.
"Between the prospect of a hard Brexit hitting staffing and tuition fees saddling nurses and midwives with huge debts, you have to wonder just what Jeremy Hunt's long-term plan for the NHS in England actually is, if he has one at all."
The Tories' "folly" of an EU referendum has placed Scotland - which voted to stay in the European Union - at a crossroads, Robison said.
"One road leads to a hard Brexit, where the future of our EU staff are threatened and with it the very fabric of our NHS, and there is a clear path towards yet greater Tory cuts to Scotland.
"The other road offers us choice - the ability to choose a different future for our country.
"I choose independence, I choose the road where we can protect our European staff, deliver our vision for the future and ensure the future of an NHS that is publicly owned, publicly run and free at the point of use."
Robison said this "is a choice that is our right to make" and told SNP activists: "It's a choice that we can and will deliver."