Very difficult – they only show up on hpi if the nice log book loan company registers it – and guess what – they do not always do it.
The only way is to check when the logbook was issued – if it is newer than the last change of keeper then there is a risk – as you can apply for a new logbook whenever you want to pay the fee for “loosing” the old one, and then just sell the vehicle.
log book is not proof of ownership – actually nothing is proof of ownership..
You can look around for advice – but last time I checked there was nothing you can really do – even dealers can be caught out – and then it is up to them to sort it out – there is nothing you can do.
Its bad sh1t and needs legislation to sort it out