Prime Minister Boris Johnson met with the leaders of the devolved nations and promised the inquiry into Covid will have a "proper Welsh dimension".
There have been numerous complaints about a lack of communications between Downing Street and the devolved governments.
On Monday, the Prime Minister met with the First Ministers of Scotland, Wales and Northern Ireland and deputy First Minister of Northern Ireland to discuss the United Kingdom’s Covid recovery and preparations for COP26.
Read more: The things a Covid inquiry must absolutely look at
Minister for Intergovernmental Relations, Michael Gove and health secretary Sajid Javid were also on the call along with Wales' health minister Eluned Morgan.
Downing Street said Mr Johnson opened the meeting by welcoming the opportunity to discuss issues together for the benefit of the whole of the UK including the vaccine rollout and the resettlement of Afghan refugees across the UK as demonstration of shared successes.
Mr Gove said that "continued collaboration" was needed to aid covid recovery and deliver for all citizens while Mr Javid said there needed to be "continued regular contact" as the covid vaccine booster programme is implemented across the UK.
Plans for a Covid inquiry were also discussed. Mr Johnson and Mr Drakeford agree that it should be a UK wide inquiry. The devolved leaders were told they would be "consulted" on the terms of reference for that.
Ahead of next month's COP26 summit, there were discussions on that.
The Prime Minister also told the leaders he was committed to "further close working and looked forward to future discussions in this format".
After the meeting Mr Drakeford tweeted: "Today I pressed the PM for a guarantee the UK Covid inquiry would properly examine the actions of @WelshGovernment and experiences of the people of Wales. The PM confirmed there will be a proper Welsh dimension to the inquiry and spoke of its importance to the whole of the UK."
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