Theresa May revealed she has begun preparations for Britain's "orderly departure" from the European Union as she held talks with her Italian counterpart in Rome.
The Prime Minister insisted Britain would maintain "close" economic links following Brexit after meeting Matteo Renzi.
Italy's premier said the negotiations must be as "efficient as possible" and called for a timeline to be set out.
"It's in everybody's interest to succeed in the end, to succeed in having a vision or a specific timeline which will make this pass easier," he said.
"We must ensure that everything is as clear as possible. We must rid ourselves of uncertainties with regard to the decision that was made by the United Kingdom to leave the institutions of the 28 countries of the European Union.
"Of course we are saddened by this and we, to a certain extent, understand the public opinion.
Importance of maintaining the closest possible economic ties
"It's a decision that was made by the British people and we respect it, however painful it is. Now we have to deal with it with common sense."
She said: "On Brexit, we have agreed on the importance of maintaining the closest possible economic ties once the UK leaves the EU.
"Italy is the UK's eighth largest export market and trade in goods alone was worth £24 billion last year."
Mrs May said she had an "open mind" about Britain's future outside the EU and suggested the country should have its own bespoke model rather than following the examples of other nations like Norway which are outside the bloc.
The PM reiterated her insistence that the UK must be able to control immigration but also get the "best possible deal" in terms of the economy.
Best possible deal in relation to trade in goods and services
She said: "We had a very clear message from the British people in the Brexit vote that they want us to bring in some control on free movement, they don't want free movement rules for movement of people from the European Union member states into the UK to operate as they have done in the past. And we will deliver on that.
"But on the other side we do of course need to ensure that we get the best possible deal in relation to trade in goods and services.
"And I am looking at this with an open mind, I think we should be developing the model that suits the United Kingdom and the European Union, not adopting necessarily a model that's on the shelf already."
She said it was important to ensure that "we can maintain that economic relationship which has been of benefit to us in the past and we want to ensure that we can continue and build on it in the future".
Mr Renzi said Britain could count on Italy's collaboration to make its exit from the EU work but called for a clear timeline to be set out.
He said: "We are interested as the Italian government to work together, to collaborate, and you can really count on our collaboration in order to make this path the most effective possible.
"This is certainly a difficult avenue because it is the very first time and so there are also procedural aspects which have to be clarified but it is in the interest of all with no exceptions to be able to have a clear timeline which will streamline this procedure."