Need to have Sainsbury's default removed (debt is settled)

I need to get a default removed as it is impacting my credibility to get a job. I usually work in the Financial Services Sector, on a contract basis. So credit checks are the norm there but they have a restricted their conditions recently. So despite working in this bank for 5 years on previous occasions, the offer of a 10 week contract was withdrawn last month, because of a credit check failure. This has been detrimental for myself and my family as I am now without a job.
The credit check failed because of a default placed by Sainsbury's Bank 3 years ago. This happened soon after my husband was taken ill and had to go through treatments for 6 months. His employers did not provide any sick pay, so we hit a financial low.
We had been paying the minimum contractual payments so far, however, when a Debt Management Company approached us and said they could help us out with the credit cards payments, we agreed. They put us on a DMP with all our credit card lenders in February 2012. They also advised not to have contact with the credit card lenders. All the lenders agreed to the arrangement.
The DMC missed the March 2012 payment and paid a token payment for April 2012, as they were slow in the process of setting up the DMP, but they also missed a payment in July 2012.
This instigated Sainsbury’s to write threatening letters, notices of bailiffs and harassing calls. Then they applied the default without notifying us.
By November 2012, I had changed jobs and my husband had resumed full time work, so we were able to make partial settlements with some of the credit cards, though I still had to sell some jewellery and borrow from family. The cards I settled had sent default notices but didn't apply a default as I settled the debt within the 28 days of the notice.
I also partially settled with Sainsbury's Bank but because they had passed on the debt to Blair, Oliver & Scott and then Wescot, it took longer to sort out and pay off. I paid this off by the end of February 2013.
They refused to remove the default despite contacting them many times in the last three years, via phone and email. They still send me statements every 6 months to say I am in arrears, and I need to pay them, even though Wescot said I would not be pursued by Sainsbury’s for the remaining amount. No other lender does this.
Since I have no job at the moment I have had more time to look into the credit file held by all 3 CRAs. I have been reading the posts on this forum and looking at the Guidance for Defaults by the ICO.
I don’t think they have complied with the principles and guidance given in these documents issued by the Information Commissioners Office.
According to this, there are many inconsistencies in the way the Sainsbury’s Bank dealt with my situation.
When I look into the credit files, there are so many anomalies, I’m confused as to why they are recorded this way. The balances are not consistent between Equifax and Callcredit and only Barclaycard recorded this as “Arrangement to Pay” on my credit file.

As the Customer Relations team were refusing to accept my request, I emailed the CEO with my grievances which were:
When an agreement for reduced payments set up in April 2012, why was the debt was passed to Wescot, 2 months later?
Why wasn’t an intention to default or default notice not sent?
Why way the default was applied too early?
Why do I get an arrears statement every 6 months?
However the Executive Complaints team passed this back to the Customer Relations team.
A lady called me from this team, this Wednesday, to say they still refuse to remove the default.
The reasons do not add up and are basically excuses to cover up their aggressive and rushed actions.

She said the default added was because the missed/reduced payments that add up to 4 contractual payments – this is incorrect. How can one missed payments and one low payment add up to that? Also the purpose of a Debt Management Plan is to prevent a default as reduced payments should be registered as Agreed Payments, but this was not applied on my credit file. Only one lender showed this.
She advised that they do not have a copy of the Default Notice but she could send a Template out.
How is that possible? I have all the letters sent to me by Sainsbury’s Bank, but they don’t. Also why wasn’t an Intention to Default sent out first? Why does Sainsbury’s Bank say they have issued a Default Notice when they have no record of it? They already said in a letter that there was no Default Notice, just a default was applied.

She accepted that they don’t even have the original agreement.
Isn't this a breach of the Data Protection Act then?

She ended the conversation that she could give me £100 compensation, which I refused, and that she would pass her report on to the Executive Office who would then write to me.

I just need some advice. Should I contact the Executive Complaints Team again?

I don’t understand what to do. I have written to the ICO but have had no response yet.