I spoke to the finance department at Oxford, not sure if this rings true for CTC but I was told that they know how long the application for the loan can take and as long as you can show that it is being processed and you have met the requirements they are generally happy to take you on until the loan is approved.
I think they prefer you to have the money for the deposit though but I'm sure they will understand if you can't scrape that together. A girl I know on the MPL course this year said someone on her course only got the loan sorted last month and applied for it this time last year! So they do understand that the loan can take a while to get sorted.
Hope this puts your mind at rest but as I said I'd check with CTC first!