Here's a round-up of key points in the PM's Florence speech and reaction to it:
- Transition period could be around two years, during which time access to the single market will continue on current terms
- Mrs May proposes a "bold new security agreement" between the UK and EU
- On trade, the PM says both sides could do "so much better" than adopting existing models
- The UK would honour commitments made while it remains a member
- There was "no need to impose tariffs where there are none now"
- EU chief Brexit negotiator Michel Barnier described the speech as "constructive"
- He said the prime minister had shown "a willingness to move forward"
- Labour leader Jeremy Corbyn said the speech suggested the PM had faced up to the reality "that Britain needs a transition to provide stability for businesses and workers"
- But former UKIP leader Nigel Farage said: "Theresa May's vision is that we leave the European Union but we do it in name only."