Background Screening/CV

Hi, can someone offer their advice please? I've just been offered a new job with a bank and they're sending out my contract with the start date, meaning I need to hand in my notice at my current job ASAP. They told me that I've passed my background checks for criminal records/credit checks etc but I still need to pass my employment check.

Here's the problem - when I originally submitted my CV, I put on there that I had been working somewhere until October, when actually it was August, and I was unemployed in this time. I've put the correct information on my online screening form, which is fine, but does anybody know if they'll check this data against my cv and notice the difference? I have no concerns about my last or current employment as they are fine. It's just this one that I'm worried about and I don't know what to do because they're expecting me to hand in my notice, but I don't want to do it until I know for sure that I've passed all of the screening.

Any advice please, besides the usual "don't put inaccurate data on your cv"?