The first step of disputing should be to send in a dispute form, also called a TC846. Download form TC846. A letter will do instead, but this form is quick and pretty easy.
Do not spend too long filling it in, and in fact use the form to demand answers rather than give too many details about your own defence. Do not provide full detail on every issue at this stage as 'new information and evidence' is required to continue to the later stages of dispute, so I recommend holding back most information at this stage.
Suggested content for filling in the TC846 form:
Take a copy/photo/scan and then get the form sent in by recorded delivery to the address at the top of the form as soon as you can.
If you are currently making repayments towards the overpayment stop them once you have returned this form. A 'suspension' of recovery/repayment demands is normal during this stage, and should be demanded if you continue to receive demands.
This stage is only over if and when they write to inform you they deny your dispute. Until they make this statement, all the other external agencies you can present your case to will keep bouncing your case back to HMRC.
Now, immediately move on to Dispute Step 1b and Claim Your Data!