Theresa May has vowed that the UK will honour its budget commitments to the EU, proposing a time-limited implementation period after Brexit of around two years during which the UK would stay bound by EU rules.

In a bid to advance stalled talks with Brussels, the British prime minister used her much-anticipated speech in Florence to make an impassioned appeal to EU leaders for a positive approach to future relations once the UK leaves the union in March 2019.

“Let us be creative as well as practical, in designing an ambitious economic partnership which respects the freedoms and principles of the EU and the wishes of the British people. And I believe there are good reasons for this level of optimism and ambition,” May said, repeating her previous assurance that the UK was “leaving the EU, but not leaving Europe”.

She also outlined proposals for a new EU-UK security treaty – and to enshrine EU migrants’ rights into UK law, taking account of European court judgements.

Facing a small protest outside, May said she hoped an agreement on citizens’ rights was close. There would still be freedom of movement into the UK for people from the EU after Brexit, but they would need to register.

The UK government has come to accept the need for a transition, or implementation, period after Brexit to avoid a “cliff-edge” crash out of the EU and to allow businesses time to adjust to leaving the EU’s Single Market and Customs Union.

Addressing the crucial question of money towards the end of her speech – the so-called divorce bill – May sought to reassure, saying she was aware of the uncertainty caused by Brexit.

“I do not want our partners to fear that they will need to pay more or receive less over the remainder of the current budget plan as the result of our decision to leave. The UK will honour commitments we have made during the period of our membership,” she said.

The prime minister added that Britain would continue to pay for EU programmes it remained part of – and would meet any eventual outcome of the Brexit talks.

Her speech was carefully tuned to her domestic UK audience after much division in her Cabinet and the country. Leading pro-Brexit figures in the government, Boris Johnson and Michael Gove, both tweeted their enthusiasm for what May said. But former UKIP leader Nigel Farage dismissed it as seeking to “appease the Brussels elite”.

The real test in terms of unblocking the Brexit talks will be the effect the speech has in Brussels and other European capitals. The EU Commission’s chief negotiator tweeted that he found it “constructive”, but more was needed to make meaningful progress.

EU leaders from the 27 member states will decide at a summit in late October whether “sufficient progress” has been made on priority issues – the divorce bill, citizens’ rights and the Irish border – in order to move on to the next stage of talks covering future EU-UK ties post-Brexit.

“We want to be your strongest friend and partner as the EU and the UK thrive side by side.” – PM’s Florence speech https://t.co/nNq8kNLPcb — UK Prime Minister (@Number10gov) September 22, 2017

Watch the speech in full

Constructive #FlorenceSpeech by PM May; must be translated into negotiating positions to make meaningful progress https://t.co/fCfBrqNhAp — Michel Barnier (@MichelBarnier) September 22, 2017

PM speech was positive, optimistic & dynamic – and rightly disposes of the Norway option! Forwards! — Boris Johnson (@BorisJohnson) September 22, 2017

An excellent speech from the PM in Florence – delivering on the wishes of the British people — Michael Gove (@michaelgove) September 22, 2017

PM didn’t need to go to Florence to accept that Labour is right about Brexit transitional arrangements. Not much else in the speech. — Keir Starmer (@Keir_Starmer) September 22, 2017