THERESA May could be about to face another Brexit battle after a number of EU member states protested about access to British waters for European fishing fleets.

During the heated talks that resulted in the 585-page draft agreement, published on Wednesday, British negotiators managed to get their counterparts in Brussels to agree to push back the discussion on access to UK waters.

The text of document says only that the EU and the UK will, at some point in the future, use their “best endeavours to conclude and ratify ‘an agreement’ on access to waters and fishing opportunities.”

Reports indicate that France, Spain, Belgium, Denmark and Portugal are unhappy that the EU has not demanded access to British fishing waters in the withdrawal agreement.

Italy, the Netherlands, Denmark and Germany have also expressed concerns that the EU’s offer of a customs union to avoid a hard border in Ireland may give Britain an economic advantage over European countries.

On Thursday night representatives from France and the Netherlands demanded that Michel Barnier, the EU’s lead negotiator, reopen negotiations on fishing and impose tougher “level playing field” rules.

According to diplomatic notes, representatives from France demanded a “guarantee that there should be a fisheries agreement giving French and other European fishing fleets access to British waters.”

They said it would be a problem for France to grant the UK access to the single market through the backstop, without Britain reciprocating access to its waters in return.

Spain, Belgium, Ireland, Portugal, and Denmark also raised similar concerns.

A European diplomat told AFP: “You could argue that because of the customs union, British fish has access tariff free to the single market. Fish is a real issue. You know fishing communities, you know how vocal they are. Same thing on the UK side.”

On Wednesday, the 13 Scottish Tory MPs told May that they would not be able to support a deal that would mean the UK was anything other than an independent coastal state.

Though David Mundell said he was “content” with the agreement, Brexiteer Aberdeen South MP Ross Thomson was unhappy.

“Under the proposed deal, the UK is merely consulted about the management of the Common Fisheries Policy. We do not take back control of our fisheries during transition. This is despite this being the default under international law,” he wrote on Twitter.

Meanwhile, the Irish have warned Tory Brexiteers jostling for position that there will be little chance of amending the draft withdrawal agreement.

Taoiseach Leo Varadkar made clear the deal being put in front of MPs was the only way for Britain to leave the EU and avoid a hard border on the island of Ireland.

He said after the tumultuous week, pragmatic MPs would back May.

“This is a withdrawal agreement which took the best part of two years to negotiate involving 28 countries all of whom have their own particular concerns and interests,” he said.

“If you start trying to amend it or unthink it you might find that the whole thing unravels.”

That view was echoed by others.

The Austrian chancellor, Sebastian Kurz, told reporters in Brussels: “It is a good deal for both sides. Nobody has been cheated. This deal prevents a hard Brexit. Therefore it helps us in Europe, but even more so it helps Great Britain because a hard Brexit would hit Great Britain significantly more severely.”

Dutch prime minister, Mark Rutte said it would be “highly unlikely” that the EU would “make important changes to these proposals.”

“We have talked about this for so long, everybody has been heavily involved,” he added.