You need to declare a 'financial disassociation' between yourself and your former partner. Go here:
http://www.experian.co.uk/
This site has pages which don't have 'linkable' addresses, so here's what you need to do:
Click 'Consumer Advice'
Click 'Questions'
Click 'About Your Credit Report'
Click 'Other People'
Under "Can I get other people's information removed from my credit report?", click the 'Online' link.
Complete the form and click 'Submit'.
That process is all that is required to notify Experian (which is one of the three main credit reference agencies in the UK) of your financial disassociation. Experian should automatically pass this information on to Equifax and CallCredit but, if you want to make sure, you could always download copies of the 'by post' form and send them to these two other credit reference agencies. (The addresses are below the links for the online and postal forms. It won't matter that you use Experian's form to send to the other two companies).
Chris