The creditor can enforce the debt in two ways.
1- Apply for a charging order. This is effectively a charge (lien) against the property.
2 - Petition you for bankruptcy if the amount owed is more than £750.00
In both cases your creditor can apply for an order of sale of the property. Only your share of the property is at risk, in both cases your wife's interest is ring fenced so (if it came to it) her interest in the proceeds of sale of the property would still go to her.
In both cases you would have a chance to defend the applicaiton at a hearing. If it is the case that you require the family home to house your children then a court will only make an order for sale reluctantly. You would have to show that you would not be able to to easily accomodate your family elsewhere.
In the case of bankruptcy you can ask the trustee in bankruptcy to postpone the sale of the house (if this is to be done) until the end of the first year of bankruptcy.
Essentially though, being in joint names does not protect it from the creditors but your wife's interest is protected if the debt is only in your sole name.
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