In a statement released by 10 Downing Street after her meeting with leaders of Scotland, Wales and Northern Ireland this morning, May said "Working together, the nations of the United Kingdom will make a success of leaving the European Union - and we will further strengthen our own unique and enduring union as we do so".
She said "the great union between us has been the cornerstone of our prosperity in the past and it is absolutely vital to our success in the future. The country is facing a negotiation of tremendous importance and it is imperative that the devolved administrations play their part in making it work".
Business Secretary Greg Clark also outlined the government's new industrial strategy and called upon the devolved administrations to play a part in helping to shape it, Downing Street said.
It also said May wanted the Joint Ministerial Council meetings to take place more regularly and would set up another session early next year.
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May has offered to involve Scotland, Wales and Northern Ireland in regular formal talks on the Brexit process but she has ruled out allowing special deals for the three units.
He told BBC Radio 4's Today programme, "Nicola Sturgeon has been absolutely clear that we must keep all options open. It would range from independence and other options would be available too. Of course independence has to be an option. It would be ridiculous to say it shouldn't be. We have been put in a situation we didn't ask to be in".
May said, "I am determined that as we make a success of our exit from the European Union, we in turn further strengthen our own enduring union. The great union between us has been the cornerstone of our prosperity in the past - and it is absolutely vital to our success in the future".
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