Prime Minister David Cameron has claimed Scots do not want to live or work in a "foreign country" after independence.
He was speaking as he met secondary school pupils in Lockerbie, about 20 miles from the border with England.
The union means people on both sides benefit from the "precious asset" of London, the Tory leader said.
"Of course I am deeply concerned that we get the right result," he said during a visit to Lockerbie Ice Rink.
"Alex Salmond (the Scottish First Minister) is making an extraordinary argument. London is an enormous and precious asset for the whole of the UK, and many Scots benefit from London's hub status and from working and investing in London and from the investment from London into Scotland.
"Now surely we should be making the most out of that connectivity, rather than separating ourselves from it.
"People in Scotland say to me 'I've got children working or studying in London', and people in London say to me 'I've got children working or studying in Scotland'. Do we really want to have a situation where they are working or studying in a foreign country?"
Lockerbie Academy recently voted 70% in favour of remaining in the UK in a mock referendum.
Senior pupils will get a chance to vote in a major poll for the first time after the Scottish Parliament agreed to extend the voting franchise to 16 and 17-year-olds for the referendum.
The most recent national poll suggests 44% support independence and 56% back remaining part of the UK.
Earlier, the Prime Minister pledged to deliver more powers to Holyrood if there is a No vote on September 18.
It would be "desirable" to legislate in the first year of the first Westminster parliament, he told the BBC.
"I don't see any reason why it shouldn't happen very early in the parliament," he said.
"The only reason I haven't given a specific pledge is each of the parties has got to set out their plans, we need to have a general election, we need to see the result of that election and then if I was prime minister I'd want to try and proceed as I have done so far on the basis of building consensus."
The Prime Minister did not give details about what the further powers could be.
But when asked if he was talking about legislating in the first year of a second term, he said: "If that was possible then that would be obviously desirable.
"The only reason I haven't given a specific pledge is as I say, I think you need to seek agreement between the parties so that what you put forward has the broadest possible support in Scotland."
Mr Cameron also looked ahead to the European Parliament election next week, arguing that most Scots back his plan for an in/out referendum on EU membership.
"The interesting thing is that in Scotland there's a majority of people who want to see that reform of the European Union, who want to see that referendum," he said.
"So it's not just the right thing to do for Britain, I think it also has the support of the people."
The Prime Minister was on the last leg of his two-day visit to Scotland, also taking in a visit to an Army barracks in Glasgow yesterday.