- Video report by ITV News Political Editor Robert Peston
Nicola Sturgeon and Theresa May have clashed over the timing of a second Scottish independence referendum during talks about the Brexit timetable in Scotland.
First Minister Mrs Sturgeon said the prime minister confirmed the terms of the UK's divorce from the EU and the details of a new free trade deal will be clear within an "18 month to two-year timeframe".
Mrs May is opposed to Scottish voters going to the polls between autumn 2018 and spring 2019, as Mrs Sturgeon has proposed.
The PM said a referendum during that period would be "unfair" to voters because they would not have all the necessary information to make a choice.
ITV News Political Editor Robert Peston said Downing Street confirmed the projected timetable for Brexit but said the government is seeking a longer period before a potential second referendum is held.
The meeting between the Conservative and SNP leader in Glasgow came in a highly significant week for both political issues.
The Scottish Parliament is due to pass a vote on a new independence referendum on Tuesday, a day before Mrs May triggers Article 50 to begin Brexit negotiations.
Mrs May, who recently said "now is not the time" for another independence vote, vowed in a speech to not let the UK become "looser and weaker".
She gave a speech to staff at the East Kilbride base of the UK's Department for International Development ahead of a bilateral meeting with Scotland's First Minister.
There the Prime Minister talked about the "great union" of England, Scotland, Northern Ireland, and Wales as an "unstoppable force".
She said: "That is why the Plan for Britain I have set out, a plan to get the right deal for Britain abroad as well as a better deal for ordinary, working people at home, has as its heart one over-arching goal: to build a more united nation.
"Because I believe when we work together, there is no limit to what we can do.
"In Scotland, Wales and Northern Ireland that means fully respecting, and indeed strengthening, the devolution settlements. But never allowing our Union to become looser and weaker, or our people to drift apart.
"So in those policy areas where the UK Government holds responsibility, I am determined that we will put the interests of the union, both the parts and the whole, at the heart of our decision-making."
The prime minister also told staff their work shows that Britain is a "big country that will never let down, or turn our back on, those in need".
She said UK aid is a "badge of hope" for many across the world and when all nations in the UK work together they are an "unstoppable force".
Meanwhile, Labour's shadow Brexit secretary has warned Mrs May must "face down" hardline Brexiteers in her own government.
Sir Keir Starmer, who has announced Labour six tests for a Brexit deal, said they risk taking Britain into a "disastrous and divisive" new reality following withdrawal from the EU.
He anticipated splits emerging within the Conservatives over the two-year negotiation period, which could result in the prime minister being forced to go back and renegotiate if she presents Parliament with a bad deal.