Pre employment checks

I have recently been offered a role with Morgan Stanley and have been advised I need to undergo a range of background checks including a credit check.

I have a fairly rubbish credit history and have a default on my account registered in February of this year. This was as a result of stupidity on my part - got into a mini dispute with a credit card company and didn't pay for a few months. The debt is currently sitting at £3400. I have now entered into an agreement with the company and have started to pay this back in the past few months.

I have other accounts - credit card, mobile, etc and all are up to date.

I would hate for my default to stop me from taking my dream job.

Does anyone know what effect this will have? In order to make my start date, I will need to hand in notice fairly quickly to my current employer but am hesitant to hand in notice whilst my offer could still fall through.