The terms 'deposit' and 'part payment' are likely to be treated differently by a court. If a person solely makes a 'part payment' then you'd have no right to retain it if that person then voids the contract to pay the remainder of the money.
However if that person paid you a deposit and knew (or could reasonably be expected to know) that the deposit was non-refundable, then you'd have the right to keep it.
Only a court could decide either way but my feeling is that (unless you both
agreed that the deposit would be non-refundable) a court would rule that you've only received a 'part payment' and therefore that you're obliged to refund it.
This blog post (from a solicitor) deals with business-to-business contracts but I suspect that a court would probably rule the same way in respect of private contracts:
http://www.business-lawfirm.co.uk/Blog/2013/06/When-a-customer-cancels-the-contract-can-your-business-keep-the-deposit-paid/
However I see no reason why you couldn't offer the vehicle for sale elsewhere as, by failing to meet the agreed date for payment, the potential purchaser has clearly voided any contract he may have had with you.