Other countries are “queuing up” to sign trade deals with the UK once it leaves the EU, Boris Johnson has said.
The foreign secretary also said the UK would not be “hauling up the drawbridge” despite new migration controls promised by Theresa May.
Mrs May set out her Brexit strategy – which includes pulling out of the EU single market – in a speech on Tuesday.
She also warned the EU not to try to “punish” the UK, saying she would walk away unless the right deal was offered.
Writing in the Daily Telegraph, Mr Johnson said: “We will no longer be part of the common commercial policy, or bound by the Common External Tariff, and we will no longer have our trade policy run by the EU commission.
“That means – crucially – that we will be able to do new free trade deals with countries around the world. They are already queuing up.
“Under EU rules, we are not formally allowed to negotiate these new treaties until we leave. But there is nothing to say that ideas cannot be pencilled in.”
Mr Johnson also said the UK would “continue to share European values”.
“We will continue the joyous exploration of other European culture and civilisation that has been expanding ever since the dawn of cheap air travel, and we will continue to welcome vast numbers of EU tourists to the UK.
“We are not slamming the door to migrants, or hauling up the drawbridge.”
EU leaders are set to give their verdicts to Mrs May’s speech on Wednesday.
Downing Street said the leaders had welcomed the “clarity” of her plans during a series of private phonecalls after the speech.
In her speech, Mrs May said it was not her intention to “undermine” the EU or the single market, but she warned against a “punitive” reaction to Brexit.
She suggested the UK could cut its corporate tax rates to compete with the EU if denied access to the single market, and added that “no deal for Britain is better than a bad deal for Britain”.