Brittle signalled his disapproval of the agreement immediately after the announcement on Thursday night that the RFU president, John Richardson, had finalised a deal with England's leading 24 clubs to end the long-running conflict.
"I am taking a few days to consider the implications," Brittle said. He must now decide whether to activate his threat to call a special general meeting of the RFU, the third in 14 months.
Hallett said: "I hope Cliff Brittle will reconsider his position as he has worked harder than anybody to drive a deal that keeps the governing body in the right place, and the clubs together as well.
"There is the prospect of a special general meeting when peace has broken out and this is something that the whole game can rejoice about. Cliff will be thinking about it but I hope he can get on with the game.
"He fought very hard to tighten the screw a little bit tighter. We felt the game could no longer take any difficulties and really had to move forward. I think Cliff is a man of integrity. He has seen something in this agreement that isn't perfect and he's a perfectionist."
The full committee of the RFU gave their backing to Richardson at the emergency meeting on Thursday and Charles Levison, a member of the English Professional Rugby Union Clubs' negotiating team, mentioned that resignation may be an option for Brittle. "He speaks with a minority voice and whether he should resign is his decision," Levison said.
However, Brittle believes he has a mission to protect the game from the possibility of it being taken over by the millionaire owners of England's top clubs. He should have enough support to prolong his campaign and will easily gather the necessary 100 signatures from the 2,000 English clubs to call an SGM in Birmingham similar to the gathering that elected him in January last year.
The England captain, Phil de Glanville, yesterday welcomed the end of the battle to control rugby union, but asked: "Why did it take so long?"
De Glanville called for "full speed ahead," but added: "We still have to look at the details of the deal because we have seen so many false dawns."
On the field, England's third-string had no answer to Otago at Bristol last night. The New Zealand side dominated play, scoring five tries in their 42-15 victory. At one stage in the second half they scored 25 points in 12 minutes.
Paul Sampson, normally a winger for Wasps, showed his club and the England selectors that he has a bright future with a superb display at outside- half as the England's Under-21 side beat Scotland 35-26 at The Stoop yesterday.
England scored six tries in a victory that was far closer than it should have been after Scotland came back strongly in the second half.
Wales Under-21 also began the weekend in winning fashion as they scored four tries in the last 14 minutes to secure a comprehensive 44-16 victory against their Irish counterparts at Bridgend.
Emerging Wales recovered from their 56-11 beating two weeks ago with a 34-14 win over Ireland A at Pontypridd last night. The visitors scored all their points before Wales opened their account but the home forwards proved too strong and helped run in five tries.Reuse content