Help writing to my bank about removing a default

Hi

I had a student account and overdraft with my bank while at University. My degree dates were supposed to be Sept 2008 to July 2012 however I had to repeat a year and graduated in June 2013. It was my understanding that I would have use of the student account with an authorised overdraft until I graduated plus an additional year from that date to repay the overdraft.

On 24 Feb 2014 I got a call from a third party stating that I owed £308 on my overdraft, I paid this amount immediately. Recently I checked my credit file to see a default placed on that account for date of 28th Feb 2014 and then it shows that it was settled on 30 Apr 2014.

I wrote to my bank to say I recently noticed this default and asked if they would remove it as a gesture of good will. They declined to do this as the default was not a bank error and stating at the time they sent letters to say they were going to mark a default on my credit file. They also said that it was company policy to grant a further year to repay the overdraft on production of my graduation certificate. I was never asked to send them my graduation certificate but I do have one dated July 2013.

I'm wondering if anyone could help me draft a second letter to them that might encourage them to remove my default as a gesture of good will. I don't remember receiving any the default warning letters and feel like I missed out on the year's grace after graduating. I know 308 is a lot of money but at the same time the default has a serious affect on my credit file and ability to apply for a mortgage.