There would probably be very little effect on you.
You almost certainly won't be able to credit in your own name until your wife's bankruptcy is discharged. Additionally, many people are now finding (simply because of the 'credit crunch') that their existing credit facilities are being curtailed. You'd obviously be a 'prime candidate' for such action. So, for example you might owe �2000 on a credit card with a �5000 limit. After your wife's bankruptcy, you might find your limit reduced to (say) �2200. As you gradually pay off the debt, you might find that your credit limit follows the balance down.
If you've got an overdraft, the bank can cancel that facility and demand repayment in full at any time, without giving any reason. (That's got nothing to do with your wife's possible bankruptcy. It's a standard term for all overdrafts). If your wife went bankrupt, your bank
might consider calling in the overdraft but it's unlikely, since they'd probably rather make money from your continued interest payments.
Owing lots of money doesn't necessarily mean that bankruptcy is inevitable. (I owe about �10K but I've managed to avoid bankruptcy by entering into agreements to just pay off a small amount each month). It certainly shouldn't be considered without getting some independent advice first. I recommend contacting CCCS:
http://www.cccs.co.uk/
Your wife might also find this 'official' information, from the Insolvency Service, useful:
http://www.insolvency.gov.uk/guidanceleaflets/ guidetobankruptcy/guidetobankruptcy.htm
Chris