The Bill was last week approved by the Commons and under its terms Royal Mail will be privatised while the Post Office will be mutualised, giving more control to subpostmasters.
Although welcoming the mutualisation, National Federation of SubPostmasters (NFSP) general secretary George Thomson advised the government not to rush into a sale. "The government has said that it will sell when the time is right, but I hope that they will not sell until enough work has been secured for the Post Office network to ensure its future, otherwise the split is pointless."
Minister for postal affairs Ed Davey said the Bill was "good news for everyone who wants to see a successful Royal Mail and Post Office network".
The government rejected a challenge by two backbench MPs to force Royal Mail to agree to a 10-year contract to provide the Post Office with its custom.
The NFSP had also called for a 10-year agreement between the network and Royal Mail.