In civil cases the burden of proof is generally on the claimant to prove that their claim is true "on the balance of probabilities" (i.e. more likely to be true than not)
There's a requirement for the claimant to prove damages, (i.e. the monetary loss they've suffered as a result of the defendant's actions), in the case of damage to property this isn't necessarily going to involve proving that you own the property that was damaged but rather that you suffered a loss as a result of the harm to that property.
Obviously in the case of assets proving ownership is one way to do this - and arguably the most simple.
Given we're talking about a car here there's more to unpack - after all it's rather common for people not to actually own "their" cars but still be in a position to suffer losses when that car is damaged.
A logbook (or V5C to its' friends) doesn't actually prove ownership (just who the "Registered Keeper" is), that said it can form part of an overall picture towards that "balance of probabilities" I mentioned earlier. For example if the claimant has a V5C indicating that they're the registered keeper (and were at the time of the loss), the addresses match, the vehicle has no outstanding finance against it and isn't reported stolen (shown via a HPI check or similar) and no other putative owners are claiming otherwise then I'd be surprised if that wasn't sufficient to meet that balance of probabilities test. Of course a bill of sale and matching bank statements would go a long way too!
Likewise a car not actually owned might still be claimable about - so long as the claimant has suffered a loss. If the car is leased or on a Hire Purchase agreement the claimant doesn't own the car, but they're still financially on the hook for it, and a in that case a copy of the agreement, bank statements showing payments for it and the V5C is probably going to be enough there.
Not having the V5C
Where (as in this case) the owner and registered keeper is unable to produce the V5C because they've lost it, dog ate it or whatever. That's really the claimant's problem - they were the one responsible for the document and the defendant had zero influence on that with their actions.
acquiring the V5 after the claim (and therefore delaying the transfer of ownership of the vehicle to the insurance company until this has occurred)
If (and I accept it's a big "if") the claimant succeeds in establishing their losses on the car without the V5C it's not actually required when selling/transferring - it can be done in writing to DVLA
the insurance company paying car hire for the time it takes to acquire the V5
Never going to happen - this would be a clear example of a cost to the claimant that resulted from the claimant's own actions. The defendant didn't lose the V5C.
From the web site this is likely to be "within 6 weeks"
Not really relevant to the legal aspects but applying online can get it done in 5 working days
It is worth noting that the value of the car is quite low, such that the costs of getting the V5 (£25) and filling a claim (£85) is significant with respect to the amount of money being claimed.
As with the "car hire" point above the £25 cost is ultimately the claimant's problem. The filing and trial fees can be recovered from the defendant if the claimant wins.
PS: I'm not sure if this is a real or hypothetical situation - but this is one that has me scratching my head as to why this isn't going through insurance? The claimant's insurance company has already de facto accepted the policy holder's assertion of an insurable interest in the vehicle at the inception of the policy and absent a really good reason to question it themselves (i.e. where they think showing the policy holder lied to them is going to save them having to pay out) it would generally never even come up.
