The EU has outpaced Britain in its quest for free trade with Australia and New Zealand after member States gave the green light to start negotiations within weeks.

With Theresa May insistent that leaving the EU will involve exiting the customs union and the bloc’s external commercial policy, the announcement from Brussels opens up the possibility that the EU could enjoy better terms with the two Commonwealth nations after Brexit than the UK will.

New Zealand’s trade minister, David Parker, said the UK’s withdrawal did not diminish the huge potential gains for his country that would come from breaking down trade barriers with the remaining 27 member states.

He said: “The EU is our third-largest trading partner, with two-way trade worth more than $20bn [£10.3bn]. Even excluding the UK, our trade with the EU is worth about $16bn annually.”

The international trade secretary, Liam Fox, had recently spoken of “reinvigorating” the Commonwealth partnership with a host of trade deals after Brexit, labelled “empire 2.0” by sceptical Whitehall officials.

But the UK will not be able to start its negotiations over future trade with New Zealand and Australia until 30 March 2019. The European commission president, Jean-Claude Juncker, has vowed to complete the EU’s talks with the two countries by 31 October of that year, when his time in office expires.

Brussels is eyeing up export opportunities for motor equipment, machinery, chemicals, processed foods and services. In recent months, the EU has struck deals with Canada, Japan, Singapore, Vietnam and Mexico.

Last week May privately proposed to Ireland and to Donald Tusk, the European council president, her government’s concept of a “backstop” to avoid a hard border on the island of Ireland, which would involve the UK temporarily staying in the customs union beyond the transition period.

It would come into force should a satisfactory free trade deal or bespoke technological solution fail to emerge that can solve the border problem. Formal negotiations in Brussels restarted on Tuesday and are scheduled to last until Thursday.

However, in a sign that the Brexiters in the cabinet are no closer to accepting the idea of staying in a customs union, the environment secretary, Michael Gove, was insistent on Tuesday morning that it could only be a temporary solution.

He told BBC Radio 4’s Today programme: “It means what it says on the tin. That temporary means not permanent. It means for a short period of time.

“I’m not going to pre-empt the eventual position that we take after we have negotiated with the European Union and with Ireland … In the same way as when you move house, a bridging loan is meant to be temporary, but whether that’s weeks or months, we don’t know precisely.”

The EU has made it clear before its negotiations with Australia and New Zealand that the size of its market offers bountiful opportunities, without the need for the bloc to expose its agricultural sector to cheap imports.

The mandate given to the commission for the talks, due to be formally launched in Wellington and Canberra next month, envisages special treatment for agricultural goods in order to protect European producers.

In contrast, there are some voices in the Brexiter wing of the Conservative party who would like to radically liberalise the farming sector in the UK, and open it up to challenge from highly efficient antipodean agricultural exporters.

Responding after EU foreign ministers announced the talks, Cecilia Malmström, the European commissioner for trade, said: “Together, we will now negotiate win-win trade deals that create new opportunities for our businesses, as well as safeguard high standards in key areas such as sustainable development.

“Starting these talks between likeminded partners sends a strong signal at a time where many are taking the easy road of protectionism.”