From my personal dealings they seem to vary the point at which security is demanded.My case over £20k they wanted security.
Also another word of advice is get the application done ASAP,
Well in advance of your proposed course start so you arn't left in the lurch.I started my application 6months before my course and was told they had 1 student joinging Oxford's APP asking for the money 2 weeks before his course commenced!!

Surprised got through selection tests with common sense like that!! LOL
Regards