Reading between the lines, I'd say that this is the remainder of one of Northern Rock's infamous Together mortgages.
They were made up of two parts, one secured against the property and the other as an unsecured loan.
The traditional mortgage element that was secured against the property could be repaid independently of the unsecured element. That would appear to have been cleared by the proceeds from the sale of your property, leaving the remaining unsecured element as the part in negative equity.
However, while the unsecured loan would have originally been charged at the same rate as the mortgage, that rate will have risen once the mortgage was paid off.
As you no longer own a property there is no way to remortgage to a better rate, so you would need to see if there was any way to raise finance on an unsecured basis at a better rate. While unsecured loan rates can be cheaper, the maximum term is likely to be only five to seven years, which would increase the monthly repayments enormously.
If you have any spare cash at all, attempting to overpay to reduce the loan more rapidly makes a lot of sense, but it is easier said than done.