Id ask the previous owner to ring the dvla stating that he lost the log book, and never sent it off with the box ticked to say its been scrapped. Or maybe get him to write a letter or declaration or something. Im sure theres something that can be done here if you speak to the right people. if you or the previous owner explain that neither of you sent them the log book, then surely they should just issue a new one to you.

If they say theres nothing that can be done, then what if someone steals your log book, then sends it off as scrapped? Is the car then useless, because thats what they seem to be saying. Strange.

Also, ask to see the log book that was sent in, or at least a copy of the signature. Then get a smaple signiture from both the new owner and the previous owner as proof it was neither of them that signed it.