The RFU were looking for further investment and were considering selling their base at Twickenham and buying a 50 per cent stake in Wembley, according to documents seen by the BBC.
Those plans were put on hold in favour of a £663m redevelopment of the stadium under the Twickenham Stadium Masterplan Programme (TSMP).
Woodward said Twickenham should be judged on the same level as other iconic sporting venues such as Lord’s, Wimbledon and Wembley, whose names have not been tarnished by commercialism.
“They didn’t sell the Championship or the naming rights to Centre Court. They understand the value of the brand,” said the 68-year-old, who coached England from 1997 to 2004.
“I take no comfort in the fact that Ireland, Wales and Scotland have sold the naming rights to their stadiums. England should not be proud.”
Asked how much the Allianz deal was worth, Sweeney said: “It’s a multi-year deal and well over £100m. It’s a fair value given the expectations for stadium naming rights these days.”
London Irish, Wasps and Worcester have all entered administration for the 2022-23 season.
“It’s money we have to put back into the game,” Sweeney added.
“We have had a hard time coming out of the coronavirus crisis and the football industry is under pressure. We have seen three professional clubs close and that has been really painful.
“So, this is the money we need to generate to reinvest in community games so that the pipeline can continue to exist.”
The inclusion of Twickenham brings Allianz’s portfolio to eight stadiums worldwide.
The stadium will host the 2025 Women’s World Cup final, with the first international match under the new name set to take place on September 14 when England’s women take on reigning world champions New Zealand.