The government has been criticised for downgrading the diplomatic status of the EU's ambassador in London.
Ex-Foreign Office ministers and diplomats said the decision was petty and could set a bad precedent.
But the Foreign, Commonwealth and Development Office insisted EU delegation staff would still receive the privileges needed to do their job.
The decision is in contrast to the 142 other countries where EU ambassadors have full diplomatic status.
David Lidington, the former Conservative minister for Europe, warned that "non-recognition could set a bad precedent for regimes that hate EU ambassadors speaking up for human rights defenders".
He said the Foreign Office should not "pick a fight on this".
Tobias Ellwood, also a former Foreign Office minister and current chairman of the Commons Defence Committee described the decision as "simply petty".
"Biden commits to strengthening alliances and we engage in silly spats which will not help strengthen security and trade cooperation - we are better than this," he said.
And ex-National Security Adviser Lord Ricketts said: "This is a wholly unnecessary move which seems part of a systematic effort to signal that the UK is shunning the EU and all its works. Not in British interests."
Instead of giving the EU's ambassador, Joao Vale de Almeida, full diplomatic status, the UK wants to treat the EU delegation as representatives of an international organisation.
This means EU diplomats would not have the full protection of the Vienna Convention which gives them immunity from detention, criminal jurisdiction and taxation.
The EU argues it is not a typical international organisation because it has its own currency, judicial system and the power to make law.
Its chief Brexit negotiator Michel Barnier expressed the hope that "a clever and objective solution" could be found.
The issue is expected to be discussed by EU foreign ministers next Monday.
EU sources have pointed out that diplomacy is based on reciprocity, meaning there could be repercussions for the UK's ambassador in Brussels.
The Foreign, Commonwealth and Development Office insisted that discussions were ongoing about the status of the EU delegation.
A spokesperson said: "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."