The Prime Minister said backers must hail the "full benefits" of the UK to keep it together in her final appearance in Scotland before leaving office later this month.
She also launched a stinging attack on the SNP insisting that Nicola Sturgeon wants devolution to fail and hinted the First Minister cannot be trusted in talks.
And she made a staunch plea for her successor as Prime Minister - Boris Johnson or Jeremy Hunt - to place the union at the centre of their plans, particularly over Brexit.
The Tory leader pointed to the recent warning from Gordon Brown that the union was facing its biggest threat in 300 years.
"I think a lot of people have take the union of granted over the years and what we need to do is make the case for the union," she told an audience in Stirling.
"And if we do not make realising the full benefits of being a United Kingdom of four proud nations and one united people our priority now, then in the future it may be too late."
The Tory leader spoke out as the two candidates to replace her as Tory leader, Mr Johnson and Mr Hunt prepare to face a hustings event in Perth tomorrow evening.
But it was her dealings with Ms Sturgeon over the past three years which provoked an unusually frank response from Mrs May.
"Over the last three years I have learned that while other parties can be relied on to work with the UK Government in good faith to make devolution a success, an SNP Scottish Government will only ever seek to further the agenda of separation," she said
"That, I am afraid, is simply a fact of political life in the UK at the moment. That fact puts an additional responsibility on the UK Government."
"If we do not do all we can to realise the full benefits of the Union – no one else will. If we do not use every policy lever within our reach to strengthen that Union – no one else will."
The outgoing Prime Minister pointed to claims by the SNP claims of a "power grab" overpowers returning from Brussels to the UK over Brexit. The UK Government says some controls in areas like fishing and agriculture - which are devolved under the Scotland Act - may be retained at Westminster to protect the UK single market.
"A UK Government which had enthusiastically launched and implemented the Smith and Silk Commissions – transferring sweeping powers over tax and welfare, stood accused of using Brexit as the cloak behind which to claw-back powers over food labelling and fertiliser regulations," Mrs May said
On one level the allegation is simply absurd. On another, it highlights a challenge which faces the UK Government as it seeks to act in the best interests of the whole UK.
"Whereas the UK Government is invested in the success of devolution, it would suit the political aspirations of the present Scottish Government for devolution to fail, or to be seen to fail.
"The criticisms of the present First Minister about how our two governments interact need to be viewed in that context."