The House of Lords Committee on Recomittment that was reviewing final amendments to the Crossrail Bill appears to have finished, and readings of the Bill are now scheduled in both houses for 22nd July, the last day of parliament until October 5th. The Commons speaker is actually forbidden from packing up for the summer until both votes have happened and Royal Assent has been granted (assuming the houses vote yes, which is very likely).
So if they stick to this schedule, that's planning permission in the bag, and the funding agreement is scheduled to be signed until September. We're in the endgame on this one.
There is one final hurdle - the Lords Committee notes that the change in law allowing Crossrail to be funded by business rates hasn't happened yet:
Funding of Crossrail is very dependent on the legislation that will take into account the small part of the business rate that will provide funding. That is how the whole project was agreed. I think that the Prime Minister said in his pre-Queen’s Speech announcement in the summer that this legislation was to be protected in the coming year. If it does not happen and that legislation does not go through Parliament, the current funding mechanism for Crossrail will not be available.It is noted later that the law is very likely to pass, on the assumption Gordon Brown's government is still around to introduce it.