Can I clear a default off my credit score??

Evening all

A few years ago, I was silly and took a mobile phone contract out in my name for my partners. She decided to run up a huge bill while she was abroad that I couldn't afford to pay. The phone ended up getting cancelled etc and the debt passed on. Which I still couldn't afford to pay. My partner then told me that all of the debt etc had been transferred onto her name and credit file. For reasons unbeknown to myself I believed her. Understandably she is now my ex partner. However this phone contract has gone down as a default on my credit report. So I can't get mortgages at a normal rate or even a car on finance. I am now in a new job earning double than what I was doing and I am up to date with all bills. I've got an online shppping account that is paid well before interest starts with the buy now pay later. And a credit card which I recently paid off in full. As well as my Mobile phone

I've been trying for 2 years now to get my credit up, it is still poor on Experian but has improved and is almost at fair.

I paid roughly £400 of the £700 bill off to the debt company 2 years ago. As that was all I could afford. I've since spoken to them and they said even if I pay the rest it wouldn't change my credit score.

I would like to ask what my options are? Can I pay to have this default cleared off my score? Or if I pay the remainder will that clear it? I've just had a baby with my fianc! and this is preventing me from getting a mortgage or car. Really frustrating!!

Any advice or tips would be greatly welcomed.

Many thanks