I must complete on average a CGT return once a week and have never provided or been asked for proof of date of move out.
Basically OP what you need is
Completion Statement from purchase (if you can't find it anymore ask solicitors for a copy)
Purchase price
Cost of Solicitors for purchase
Cost of any capital improvements so the extension definitely. Shakier ground with kitchen and bathroom unless they were a significant upgrade and that doesn't just mean old version replaced with modern version. So did you put downstairs toilet in when there wasn't one before? Do you now have 12 cupboards an integrated dishwasher and an island when you just used to have 9 cupboards for example.
Completion Statement from sale
Cost of Estate Agent for sale
Cost of solicitor for sale
Work out PPR relief
Work out if you have any prior capital losses you can use (I'm going to assume not unless you have previously sold a property for a loss most people don't)
Split everything in half etc if joint owners
Apply the £3000 annual exempt amount
Job done.
Honestly the system talks you through it but if you do get stuck part way you can always get a tax adviser (not an accountant) to take over or even just help you with one particular bit