can his ex force the sale of joint home in -£

Hi I am new to this forum,
I currently live with my partner in the home he shared with his ex partner. She left 7 years ago and has not contributed to the mortgage in that time period or the secured loans they got on the property. They have a daughter together she is 8 and stays with us 2 nights a week and rest with her mum in a council house for which the mum gets lots of benefits and only pays minimal amounts.

We have tried to get her name removed from the mortgage but my partner can not take the mortgage over alone the mortgage company will not allow that and I an a full time student. We have explored all options of family coming on etc but this is not possible.
She is aware we have tried to get her removed and that with the mortgage and secured loans the property is over 20k in negative equity. We pay the mortgage and repairs for the property without issue however she is not threatening to apply to the courts to force the sale. can she do this? She is also saying that she can get me removed from the property as my name is not on the mortgage? is that possible the mortgage company know i live here as its me that pays them each month.

I offered to go to a solicitor with her and draw up a contract that once i finish my studies (14months) and I am financially stable I will do my best to remove her from the mortgage.

She is unhappy with this and it seems as she can''t get her own way with this se is now trying to cause trouble regarding access to their daughter. But thats a whole other story.

Do you mean your partner''s ex-partner is threatening to apply to court to force a sale rather than she is not?

If they weren''t married she can apply under property law to force a sale, but there isn''t a great deal of point if the property is in negative equity and she doesn''t need to raise a mortgage. Having said that it would be better to sort things out sooner rather than later.