Second the MSE recommendation a thousand times over.
Before you think about any loans or credit cards, do the Money makeover and do everything that is relevant to you, ie cut as many bills as you can, cut down discretionary spends, food and drink out of the house especially can add up enormously and vow to clear the OD.
Is it costing interest and charges? How long has it taken to get that big? If it's built up slowly over time, you might just need to make a few changes and have a lean few months to get rid of it in no time. Also sign up to the weekly email for ongoing tips to make a bit of extra cash and save money on your normal spending. As suggested it might be worth converting to a loan or credit card balance transfer if this reduces the interest/charges, MSE has details on which cards are suitable.
But if you do this you MUST MUST MUST not run the OD up again, or else you’ll end up in position where you have the big OD and have other debt too – not good. You might find it helpful to split your money into several accounts on payday:
regular direct debits
savings for annual and irregular expenses like insurance, broken washing machines etc but while you are trying to get out of debt, maybe leave this money in the bills account as it will mean that the OD is lower and cheaper.
Do not do any day to day spending from your bills account, but move a budgeted amount for essential expenditure like food, travel, DC expenses to another account to spend on a when it’s gone it’s gone basis. If you are disciplined, you could use your credit card because if you pay it off in full every month, it costs nothing and at the same time reduces the OD, saving interest/charges.
Finally, you need to make sure your DP is also on board with budgeting, and you both stick to a budgeted amount for personal spending, otherwise he will be undoing your good work if he is spending freely at an unaffordable rate.