Theresa May has said she retains an "open mind" about the UK's trading relationships after Brexit amid reports some cabinet colleagues want the UK to pull out of the EU's customs union.
During talks with Italian counterpart Matteo Renzi, the UK PM suggested she favoured bespoke arrangements rather than replicating those used by others.
"I think we should develop the model that suits the UK and EU," she said.
Mr Renzi said the EU vote was sad but he hoped "some good would come of it".
During a press conference in Rome, Mrs May confirmed that she had chaired the first meeting of the UK cabinet committee tasked with overseeing work on Brexit on Tuesday.
Mrs May, who has already visited Berlin and Paris and is scheduled to visit other EU leaders later this week, said that although the UK was leaving the EU the UK would "still very much be part of Europe".
The prime minister said Brexit meant a "new chapter" in Anglo-Italian links but she said she hoped the current £24bn annual two-way trade could be boosted and the nations would continue to co-operate within Nato, G7 and the G20 to face the "complex and global challenges" posed by terrorism and mass migration.
'Vision and precise timeline'
She restated her position that the UK would need time to prepare for official negotiations on leaving the EU and that it was her intention to guarantee the status of EU nationals already working in the UK while limiting the future free movement of EU nationals into the UK.
Pressed on suggestions by the International Trade Secretary Liam Fox - who is on a trade mission to the US - that the UK could potentially leave the EU's customs union to facilitate trade deals with other countries, Mrs May said she was "looking at this with an open mind".
The UK, she suggested, should be flexible and not look to try and emulate any other country in its dealings with the EU.
"I think we should be developing the model that suits the United Kingdom and the European Union. Not adopting, necessarily, a model that is on the shelf already."
If the UK remained part of the EU's customs union, it would not face tariffs to export most goods into the EU but it would have to accept the EU's external tariffs when trading with non-EU countries and would not have any say in setting these external tariffs.
A number of countries, including Norway and Iceland, are members of the European Economic Area but outside the customs union. They still have tariff-free access to the EU's single market via free trade agreements but those exporting to the customs union may still have to pay administrative fees and be subject to customs controls and greater paperwork.
In response, Mr Renzi said the UK's exit would be "painful" but Italy would do "its utmost to collaborate and support the process" of UK negotiations.
But he added that the talks would be "delicate" given the conflicting desire of maximising trade while restricting freedom of movement.
He said it was "important to have a vision and precise timeline for the process" but added that it would be a "message against democracy" if the consequences people voted for in the referendum didn't happen.
Mr Renzi said the EU was a "miracle" that had produced "60 years of peace and prosperity" and it was time for its members to look to the future.
Earlier on Wednesday, the European Commission said it had appointed former senior official Michel Barnier as its chief negotiator for the UK's negotiations. The UK has said it won't begin official exit discussions - known as the Article 50 process - until next year.