The Welsh government has left Nicola Sturgeon unexpectedly isolated after agreeing to sign a controversial deal with UK ministers over the sharing of EU powers after Brexit.

Mark Drakeford, the Welsh finance secretary, said significant concessions the UK government had made in the last few days were enough to protect the Welsh assembly’s powers when Britain leaves the EU.

That signals the end of a potent coalition forged last year between Scotland’s first minister and her Welsh counterpart Carwyn Jones when they united last year to accuse London of plotting an unjustifiable power grab after Brexit.

Shortly before Drakeford’s announcement, Sturgeon had written to Theresa May stating that the Scottish government remained opposed to the proposed power-sharing deal, and would not yet sign it.

In an open letter published on Tuesday afternoon, she pressed the prime minister to make further concessions on how their two governments would share powers, which include farm subsidies, fishing quotas, GM crop policies, organ transplant rules and food labelling.

The Welsh agreement means the Cabinet Office can now table its detailed amendment to the EU withdrawal bill on devolution powers in the House of Lords before a deadline of 4pm on Wednesday.

Scottish and UK ministers will hold a further, potentially decisive round of talks next week.

Welsh support for the deal suggests peers will be less willing to support Scottish demands for greater concessions when the Lords debates the new clause next week, and when they vote on it later in May.

The joint approach by Sturgeon and Jones, who is standing down in the autumn, backed publicly by the Scottish Tories, had forced May into making a series of substantial concessions on their post-Brexit powers earlier this year. May gave the Scottish and Welsh legislatures direct control over more than 100 policy areas currently controlled by the EU.

Sturgeon said on Tuesday that the new UK government offer that Westminster’s powers in these areas would lapse by 2026 were unacceptable. It gave too much power to UK ministers, many of whom would change in the next seven years, she said.

Mike Russell, the Scottish Brexit minister, told MSPs on Tuesday that it was impossible to forecast who might be prime minister and what their policies would be during that time.

Sturgeon told May the Cabinet Office’s latest concessions still showed too little trust in the Scottish government and Holyrood needed complete parity with Westminster

Russell wrote to David Lidington, the Cabinet Office minister, setting out two suggestions to resolve the crisis – either withdraw the contentious clause entirely and allow the deal to be reached by mutual consent, or agree that any changes to pan-UK policies could only happen with the explicit consent of Holyrood.

Ministers and senior officials from all three governments have spent weeks thrashing out a complex deal under which they and ministers in Northern Ireland would either control or share as many as 153 EU powers after Brexit.

UK officials had believed the Scottish government was poised to support the deal on Tuesday until Russell unexpectedly pulled out of a joint ministerial meeting in London scheduled for Tuesday afternoon. Russell was unable to dispel strong suspicions that Sturgeon vetoed the deal personally at the weekend.

Drakeford, who is a frontrunner to replace Jones as Welsh Labour leader and first minister, said: “London has changed its position so that all powers and policy areas rest in Cardiff, unless specified to be temporarily held by the UK government. These will be areas where we all agree common, UK-wide rules are needed for a functioning UK internal market.

“London’s willingness to listen to our concerns and enter serious negotiations has been welcome. In a devolved UK the respective governments need to deal with each other as equals and this agreement is a step in the right direction.”

Leanne Wood, the leader of Plaid Cymru, the Welsh nationalist party, accused Drakeford of “selling Wales down the river” in a “backroom deal with the Tories”.