The UK will get no special treatment in its future economic relationship with the EU, European ministers have said, in a further blow to Keir Starmer’s hopes of negotiating a single market for goods.

The EU’s ministers for Europe, who met on Tuesday, said they wanted deeper cooperation with the UK, but this had to be in line with fundamental principles, including no cherrypicking of EU policies, according to three diplomatic sources, who spoke about the private discussions.

The Guardian revealed last week that the government had pitched the creation of a single market for goods between the UK and EU to Brussels, but the proposal was rejected by EU officials.

A single market for goods, long hinted at by the prime minister and the chancellor, Rachel Reeves, would be a radical departure for the EU. Since the Brexit vote nearly a decade ago EU leaders have said that the single market encompassed four freedoms: free movement of goods, services, capital and people.

Europe ministers had no appetite for the British proposal of free movement of goods only, although the idea was only briefly mentioned at Tuesday’s meeting, EU sources said. “Member states reaffirmed the established legal framework underpinning the relationship and negotiations, with continued emphasis on the indivisibility of the four freedoms, balance of right and obligations, autonomy of EU decision making and the avoidance of cherrypicking,” an EU diplomat said.

The diplomat said the EU commissioner in charge of UK relations, Maroš Šefčovič, had concluded “that the EU remains united in its ambition to deepen ties, while the UK’s red lines are increasingly constraining progress”. The European Commission declined to comment.

France has said it would be willing to welcome the UK back to the European single market and customs union, reflecting the changed geopolitical landscape since Brexit. EU officials have also stressed that a customs union or alignment with the single market remains available to the UK.

But some member states are sceptical about the UK’s willingness to be a rule taker. Joining the single market, minus EU membership, would leave the UK without a vote when new rules are being drawn up.

A second EU diplomat said the relationship with the UK was “the best that we have had in a very long time” but “the UK still wants to have the cake and eat it”.

EU member states, the person said, “value and cherish” stable relations and want to work with the UK, but “this does not mean the UK and the EU are equal partners”.

Questions are growing about Starmer’s reset with the EU, with no date announced for a long-expected EU-UK summit, which is tentatively pencilled in for 13 July.

The summit is meant to finalise a sanitary and phytosanitary (SPS) agreement to ease trade in food, drink and farm products, an accord on linking emissions trading systems (ETS), and a youth experience scheme enabling young Europeans to work, study and travel across the UK and the EU.

It is also seen as a moment to launch a future agenda for cooperation, with both sides interested in deepening ties on defence.

Asked about the future EU-UK relationship, Ireland’s Europe minister, Thomas Byrne, told reporters: “We have matters to agree now: the ETS, SPS and youth experience scheme. Let’s focus on them before we get on to any other discussions, which also present difficulties. We certainly want to be as open as possible in the relationship.”

Asked specifically about the UK’s single market for goods proposal, he said: “It presents challenges.”