Mrs Knight will shortly publish a detailed version of the Bill which she hopes the Government's parliamentary business managers will agree to put to the House when a slot of half-a-day or a day comes up.
Mrs Knight also hopes that building societies will back the new version of the Bill which she believes should help convince the Government that the Bill can be slipped through without controversy.
A Treasury spokeswoman said the new draft would take account of consultations with building societies, which are anxious to have the new legislation on the statute books.
Their backing would give Mrs Knight additional weight when negotiating with business managers in the House, if a slot for an extra Bill came up. Time is quite often found for a short piece of legislation.
"We can't guarantee that space but we have a much better chance if we have something that everyone has signed up to," added the Treasury, which admitted that this was not a common way of introducing legislation.
One of the principal changes from earlier drafts is a "do as you would be done by" clause that removes the five-year immunity from takeover of a society after it has converted to a bank, if it starts buying smaller societies.
This is to prevent the new breed of converted banks gobbling up all the smaller societies while remaining immune from takeover themselves.
There is strong support among building societies for this new provision, which would come into force immediately the Bill was passed. That means it could apply to Halifax if Parliament approved it in the next few months.
There are also to be new provisions to deter carpetbaggers who put their money into societies to speculate on windfall gains on conversion.
The new features of the Bill include powers to strengthen membership conditions if a society is seriously disrupted by floods of money from carpetbaggers.
Mrs Knight said: "These proposals will bring in a better deal for societies and their customers."