"We will not accept that the United Kingdom will be the only country in the world that does not recognise the Delegation of the European Union as the equivalent of a diplomatic mission," High Representative Josep Borrell warned on Monday.
The European Union on Monday called on the UK to grant full diplomatic rights to its first-ever ambassador to Britain, stressing the delay "is not a friendly signal".
The government of Prime Minister Boris Johnson has so far refused to afford the staff of the EU's Delegation to the UK, including ambassador Joao Vale de Almeida, the same privileges as those afforded to diplomats under the Vienna Convention.
The convention awards the head of the mission and other key staff immunity from prosecution and exempts them from taxation. The mission's properties and documents are also treated as "inviolable".
Asked about the delay following a meeting of EU foreign ministers in Brussels on Monday, High representative Josep Borrell said: "There is a clear view and unity among member states" on the issue.
"It is not a friendly signal, the first one that the United Kingdom has sent to us immediately after leaving the European Union. If things have to continue like this, it is not a good prospect."
The UK's divorce from the EU was finalised on December 31 following a year-long transition period marked by turbulent negotiations over the future relationship between the two sides. An agreement was reached at the eleventh hour on Christmas Eve but it does not cover foreign policy, external security and defence cooperation.
"We do not ask for something new, we do not ask for special treatment. The external status of the European Union is recognised by countries and international organisations around the world. We expect the United Kingdom to treat the European Union Delegation accordingly and without delay," Borrell said.
"We have 143 delegations around the world. Without a single exception, all host states have accepted to grant these delegations and their staff a status equivalent to that of diplomatic missions of states under the Vienna Convention. And the UK is very well aware of that. 143 States around the world, all of them," he added.
Borrell did not signal whether the EU would take retaliatory action against the UK's mission to the bloc and its newly-appointed head, Lindsay Croisdale-Appleby but he stressed that "reciprocal treatment based on this convention is a standard practice between equal partners."
"We will give all facilities in order to look for a satisfactory manner, but we will not accept that the United Kingdom will be the only country in the world that does not recognise the Delegation of the European Union as the equivalent of a diplomatic mission," he added.
But Britain's Foreign, Commonwealth and Development Office said in a statement that "the EU, its Delegation and staff will receive the privileges and immunities necessary to enable them to carry out their work in the UK effectively."
The UK argues that the EU is an "international organisation" and not a country and that diplomatic privileges granted to such organisations are very similar to those awarded to diplomatic missions, including immunity from prosecution in certain cases and exemption from a host of taxes.
Under the Vienna Convention, a diplomatic mission is described as "representing the sending State in the receiving State". Its other functions include protecting its interests and nationals, negotiating with the government of the receiving State and "promoting friendly relations".