The area's two council leaders say a devolution deal for the Humber is still the best way forward for the region.
Their renewed determination to strike a deal with the Government comes amid continuing speculation that their South Bank counterparts are stalling over the issue.
It's believed the two Conservative-run councils are keener on linking up with neighbouring authorities to form a Greater Lincolnshire body.
More uncertainty has been added by the resignation of Northern Powerhouse minister Jake Berry who personally backed the idea of Humber deal at a meeting with all four council leaders in late January.
At that meeting, Mr Berry set a three-week deadline for them to reach an agreement.
However, that deadline has come and gone while his successor Simon Clarke has yet to sit down with the council leaders to discuss their next steps.
Speaking at this week's full council meeting, East Riding leader Councillor Richard Burton maintained his strong support for a Humber deal.
He said: "It was made clear to us that the government sees a Humber estuary deal as the only game in town and are keen to work with the four authorities on a deal across the Humber which ultimately will require the creation of a combined authority and a directly-elected may because the minister said mayors mean more money.
"Since the cabinet reshuffle Jake Berry is no longer the Northern Powerhouse minister. However, following discussions with officials it has been made clear that the government position remains the same - the government is still keen to progress a deal with the Humber."
Cllr Burton claimed there was "strong support" from the region's business sector for a Humber deal and urged his South Bank counterparts to follow suit.
"In order to meet our aspirations we need local control of key enablers and resources but, like anything new, we have some barriers to overcome in order to move forward, such as the loss of identity.
How would a combined Humber authority work?
If agreed, the new body would be led by a directly-elected mayor similar to Sadiq Khan in London or Andy Burnham in Manchester.
Funding and decision-making powers from Whitehall would be devolved to the mayor.
The mayor would work in partnership with the four councils around the estuary.
Scrutiny of the mayor's decisions and policies would be carried out by a board of senior councillors drawn from the four authorities.
What happens to the existing councils?
They will continue as they are, running the same services as now with the same make-up of councillors.
What will a Humber combined authority do?
Powers devolved elsewhere give a clue to what might be on offer here.
In Greater Manchester, the mayor has control of budgets covering adult education, business support, housing investment, skills and training and management of a post-Brexit funding pot being set up to replace financial support from European Union.
He also powers to introduce bus franchising and a big say in joint transport issues with Network Rail and Highways England.
On planning and land use, the mayor has powers to create new strategic polices for local councils to follow along with the ability to set up development corporations.
"There are concerns from colleagues on the South Bank regarding the loss of their Lincolnshire identity and there are also the governance arrangements for a combined authority, including the powers for the mayor, which need to be negotiated and agreed.
"All these will take time but we need to start and we need to find a way through because if we can, the rewards promised will be considerable and will be a potential game changer.
"I firmly believe that we need to look beyond the issue of a loss of identity and embrace this excellent opportunity which will give us access to funding, infrastructure, skills and jobs that our residents need and deserve."
City council leader Steve Brady said Hull remained firmly behind the idea of a Humber combined authority which would attract devolved funding and decision-making powers from Whitehall.
He said: "Jake Berry's resignation has clouded the issue once again but we are still being told by the civil servants that a Humber deal if the government's preferred way forward.
"We will hopefully be meeting the new minister very shortly and we will see where we go from there but what I am keen to avoid is any furether delay which ultimately puts us at the back of the queue when it comes to devolution and extra funding for the area."