The clubs are also frustrated that detailed agreements struck with the Rugby Football Union about the number of games that leading England players will play over the course of a four-year World Cup cycle will be left in disarray if the year-long competition between the two hemispheres is established.
"There is a fear that the Nations Championship proposal would throw the game into chaos and we should all work to ensure that doesn't happen," said one Premiership source.
There are also widespread concerns about the future of the European competitions if the new tournament is established as it would almost certainly leave no room for the two rounds that are currently played in October because of a later finish to Test rugby during the summer rounds of the competition and greater involvement of the top players.
"The European competitions would be in jeopardy," said another club source. "People will then say you can't have two European fixtures before the start of November because the players will still be on their rest periods."
Mark McCafferty, Premiership Rugby chief executive, in an exclusive interview with Telegraph Sport, admitted that the English clubs were frustrated that the structures agreed in San Francisco appear to have been disregarded.
"The clubs feel there has been a lack of respect shown to them," McCafferty said. "We went into San Francisco to strike a balance and that is what we did.
"The structure of international and club competitions and of the associated seasons over a four-year cycle involves a complex set of issues and needs to be finely balanced, including the player welfare aspects of that. You need expertise, experience and the right people around the table, as we did in San Francisco, to produce sensible, balanced outcomes.
"We have the next three seasons already agreed with the RFU and RPA (Rugby Players' Association) and we would say we have got a more sophisticated system of balance and player welfare management through that period which this proposal would drive us backwards from."
World Rugby appears to be prepared to drop the semi-final stages from their proposed competition as a compromise but McCafferty said even that would not be acceptable to the clubs.
"Dropping the semi-final would not make a difference to our position because I think that is a marginal issue," he added.
"The real issue is that you are potentially going from the agreed two Tests in two summer tours in a four year cycle where frontline players would not need to be involved after a World Cup or Lions tour, compared to the World Rugby position of straight after a World Cup, for example in 2024, having played a full-on Six Nations, then having to go to say New Zealand, Australia and Fiji – that is a world away from the balance achieved at San Francisco and the player rest periods we have subsequently built in.
"We are always open to sitting down with people on a level basis and saying, 'what are the real issues?', which is what we did in San Francisco
"We were quite instrumental in drawing up the fixture list and then used the RFU to get it over the line so you can do things to improve it and are happy to sit down and talk about that.
"But it is the way they (World Rugby) have gone about it and now this exclusion which makes it difficult to accept."
A World Rugby spokesperson said: "In line with the mandate of our unions and Executive Committee, the proposed Nations Championship competition model has been developed with careful and detailed evaluation and consultation with the international game's major stakeholders. With a true pathway for all unions and a robust commercial model, it has the future growth and sustainability of the global game at heart."
