Kelly has proposed a 'carry-over' motion, for the Crossrail bill to be suspended until the next session of parliament, when it will pass directly to its third reading.
"Further proceedings on the Crossrail Bill shall be suspended until the next Session of Parliament," she said.
London's Mayor Ken Livingstone outlined the shape Crossrail will take once the scheme attains Royal Assent:
"As has already been announced, Transport for London will take over sole ownership of Cross London Rail Links Limited - the company promoting and developing Crossrail - when the Crossrail Bill receives Royal Assent next year. Currently it is a joint venture between TfL and the Department for Transport.
"Second, I can confirm that all Crossrail services are programmed to come into operation over the course of twelve months from 2017. This includes the south-east section down to Abbey Wood, which is vital to open up the Thames Gateway.
"The start and subsequent build-up of services within that twelve month period will be phased to allow time for rolling stock and railway systems testing to ensure reliability. The line will be integrated into TfL's existing zonal system, all existing ticketing options such as Oyster will apply, and a premium fare above TfL zonal ones will only operate for the extension to Heathrow.
"Third, as Doug Oakervee has outlined, I am determined to ensure that people living in East London can take up the thousands of jobs that Crossrail will offer - Cross London Rail Links Limited has estimated that as many as 14,000 jobs will be created, many of these in the construction industry.
"I will ensure that the relevant agencies in London provide the right training and opportunities so that Londoners from all its diverse communities have the chance to work on this flagship project,” he said.
The Crossrail bill will not now gain any further amendments in the House of Commons, and will be printed, and pass through first and second reading stages, through committee stages directly to a third reading.
The bill will then pass to the House of Lords, where some amendments may be made. Assuming there are no significant bottlenecks, the bill will then attain Royal Assent shortly afterwards.
The next parliamentary session begins on 6 November with the Queen's speech.