Britain on Wednesday picked career diplomat Tim Barrow to replace its ambassador to the European Union, who unexpectedly resigned just weeks before Brexit negotiations are due to start, a government source told AFP.

Barrow, the former ambassador to Moscow who has previously served in Brussels, replaces Ivan Rogers who resigned on Tuesday with an email which criticised London's approach to leaving the bloc following the shock referendum result in June.

During a 30-year diplomatic career Barrow has twice served in Brussels at UKRep, the office which represents Britain in negotiations in the EU, and has also been posted to Kiev as British ambassador.

The appointment was welcomed by Tom Fletcher, Britain's former ambassador to Lebanon.

"Great news. Tenacious, human, expert, connected, thick skinned enough not to worry about nutters, and will avoid poison in the chalice," he wrote on Twitter.

Charles Grant, director for the Centre for European Reform, also viewed the appointment positively.

"Good that Tim Barrow will replace Ivan Rogers at UKREP. He is expert on EU (&Russia) & will be respected by its governments and institutions," he tweeted.

Barrow will begin his new post at a crucial time for relations between Brussels and London, as British Prime Minister Theresa May has promised to kick-start negotiations to quit the EU by the end of March.

Barrow's predecessor faced criticism last month when he said it would take 10 years for Britain to conclude a trade deal with the EU.

In a resignation note to staff Rogers said London lacked multilateral negotiating experience and urged colleagues to continue providing their expertise even when unwelcome.

"I hope you will continue to challenge ill-founded arguments and muddled thinking and that you will never be afraid to speak the truth to those in power," he wrote.

The appointment of Barrow as his replacement is expected to disappoint anti-EU campaigners, who had hoped a strong pro-Brexit candidate would be posted to Brussels.