Can I challenge a small mobile phone default bill that has tarnished my otherwise pristine credit score?

To cut a long story short. I briefly moved in with a house mate for under a year and bought an mobile data sim for my Osprey for portable WiFi.

Then due to severe depression and a yet undiagnosed mental health condition I moved back in to my original address with my mother. Prior to this, I had great credit, credit cards never missed a payment, never missed rent, never missed any bills or contracts, had a 3 car on lease with a big deposit and big monthly payments which I paid on time every time.

After I moved address I heard nothing from EE (The bills were being sent to a now vacant house) 3 months was left on the mobile data plan which I thought I had successfully cancelled and paid, so I paid 20 out of the 24 month contract.

Then after a few months I was contacted by Lowell who some home managed to magically find me at my new address (how come EE could not of done this?) as soon as I received the bill through the post I paid immediately a one of fee of £108 and thought nothing of it.

2 years later I have checked my credit rating and have been distraught to see my credit rating is hovering around the poor/stable level. If you go across my entire credit history with Equifax, clear score and Experian. You see nothing but green across the board, successful payment after successful payment with MERELY one default on a mobile data plan which I could of easily paid off if only I had known.

With regards to mental health, I was living with an undiagnosed condition which can lead to depression/forgetfulness and other undesirable traits that could lead to such minor mistakes, such as thinking I had told all my financiers I had moved address except one which was EE.

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I have now been diagnosed correctly and I'm receiving the appropriate treatment, which has improved my mental health dramatically. I would be able to back this up with a note from either the hospital, the mental health unit I am with or my own personal Doctor, all of which I believe would say leniency should be shown in this particular case as such a minor mistake could end up with me going backwards in my mental health progress which right now is in a very good place and has taken over a year of emergency treatment and medication.

I called Equifax and explained the entire situation and they were very sympathetic and opened a dispute to have the default removed and within 2 hours Lowell responded to them and I got the following reply from Equifax:

"Thanks for getting in touch today about the information on your credit report.

Lowell Portfolio 1 Ltd (I) has responded to your dispute and have told us that the default will remain for 6 years passed the default date. 

If you need more information, please contact the company directly.

The information on your credit report belongs to the data provider and we cannot change it without their authorisation. If this is the only dispute you have open the note we’d added automatically stating that your information was under dispute will be removed within the next five days. If you've raised multiple disputes the note will be removed when the last dispute has been resolved."

I mean this whole thing seems absolutely nuts to me, 6 years this stain will be on my record. Is there any possible thing I could do to help this situation. Perhaps I could call EE first then if no luck maybe Lowell.

Lowell's website does say: you can Add a note to your file If there were difficult circumstances when the default happened, you can ask the CRA to add a note onto your file. For example, if you fell into debt and your account defaulted because you were made redundant, or suffered a serious illness, you could add a note to help lenders understand the situation. This could help to offset the default’s negative impact if you need to apply for credit. is that something Equifax can do for me, with all the information I have given you, perhaps provide a note to this one exception highlighting the circumstances and informing potential future lenders why this default is here and how small of a figure it was for it to ruin my otherwise good credit rating

Any advice would be greatly appreciated