Is it your partner's ex? Do they have a financial interest in the property. I would assume you're worried about children should the property be repossessed.
It can be quite a lengthy process, dependant on the severity of arrears and circumstances, the first few court hearings will usually give a chance to keep to a repayment plan.
In order to actually evict someone to repossess and sell the property the lender would need to get a possession order at court. This is a matter of fact hearing and a date and time would be set for the bailiffs to come round and do the official eviction.
Flexibility depends on the lender and, when the account is in litigation (referred to solicitors for repossession proceedings) the solicitors acting.
I've managed to stave off some repossessions in order to allow extra time for a private sale (highly recommended as the seller may get some equity back depending on what is owed). It's not easy though and the lender/solicitors would need proof of the sale and ability to pay them off in full.
Be careful selling for a much reduced price unless it covers owing as a lender would be loathe to accept a settlement of a lower figure when they could sell it themselves and get more money back.
Difficulty comes in here is there is more than one charge or other charging orders - if there are any CCJ's or similar there may be a restriction on the property which means that the amount owing needs to be paid before sale.
The title can be downloaded from the Land Registry here for �3.00...
http://www.landregisteronline.gov.uk/
It should show all charges secured on the property.