How long will it take to repair bad credit history?

I got into a fair bit of debt and had a number of defaults. I have now paid all my debts off but the credit report will show all previous debts – one which had a ccj on it from bout 3 or 4 years ago. I am wanting to repair the history to apply for a joint mortgage but want to know best way to repair credit rating and how long it will take. Any assistance much appreciated. Thanks

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