Premier League chief executive Richard Masters says a degree of trust with EFL chairman Rick Parry will have to be re-established after his role in the hugely controversial Project Big Picture plans.

The relationship between the competitions was strained to say the least when the PBP proposals became public knowledge at the weekend.

They were developed by Liverpool and Manchester United and publicly endorsed by Parry.  While they included an immediate £250million bailout for the EFL and a 25 per cent share for the league every year in any future Premier League media revenues, they also sought to concentrate Premier League power in the hands of the so-called 'big six'.

Premier League clubs rejected PBP when they met on Wednesday, and they will instead continue work on a "strategic plan" involving all 20 teams.

They also agreed to offer an additional £50million in rescue grants and loans to clubs in League One and Two struggling without matchday income because of the coronavirus pandemic.

That money is on top of £27.2m already advanced in solidarity payments.

The Premier League's offer will now be formally submitted to the EFL for approval, and Masters said it was vital there was trust between his organisation and Parry, who has been the only public figurehead for PBP since news of the plans emerged on Sunday.

"There is some considerable frustration that that proposal got pushed in public," Masters said.

"There has to be trust between the Premier League and the EFL and we need to re-establish all of that.

"But we don't have a beef with the EFL, certainly not with its clubs. We want to have a good relationship with them. We're their biggest partner.

"We have a historic relationship with them. So we want it to be constructive."

Culture Secretary Oliver Dowden had earlier warned Parry not to be distracted by PBP, which he described as the "latest wheeze", and urged the leagues to continue talks over an EFL rescue package. He also described PBP as 'Project Power Grab'.

He has welcomed the Premier League's offer to Leagues One and Two as "a good start". The Premier League said discussions would continue over possible loans to clubs in the Championship.

Masters said the Premier League meeting on Wednesday had been "candid, constructive and positive" despite the involvement of two of the clubs in drawing up the PBP proposals.

"Whilst there has been a lot of things said and done, a lot of speculation over the last four days, I don't think it's irreparably damaged the Premier League. And I think that today's meeting proved that," Masters added.

FA chairman Greg Clarke said on Tuesday he had walked away from Big Picture discussions in the spring "when the principal aim of these discussions became the concentration of power and wealth in the hands of a few clubs with a breakaway league mooted as a threat".

However, Masters said: "I don't think anybody has been talking about breaking away."

Asked if there were any elements of PBP that could be worked with, Masters said: "Well, I think there was an acknowledgment in the room that English football's model is a huge success, but that it hasn't been reviewed or modernised for a long time.

"And so that perhaps there have been some systemic issues built up that need dealing with.

"And as I said, a lot of the things we've been talking about – league structure, calendar construction, governance, the financial regulation, broadcasting and commercial will all be part of our review process as well."

Project Big Picture has, at least, provoked a much-needed conversation which the EFL hopes can be involved in going forward.

"As we have maintained across the past 72 hours, there is a significant issue facing the English footballing pyramid and therefore it is encouraging that there is an acknowledgment that a review of the current status quo is required, with a strategic plan to be developed to consider the future of the football," said a statement.

"While by no means a finished product, Project Big Picture was developed to consider these same issues and address the challenges facing football from top to bottom.

"The EFL welcomes the opportunity to contribute to any wider debate with colleagues across the game as we seek to finally address impossible economic pressures and deliver on the objective of having a sustainable EFL in the long-term."