I had this same trouble (being in Europe and not the UK). DVLA would not send me the information. Like you, I did get some information from one of the previous owners, whose name I had on a repair receipt.
I got the most information by putting up a blog about my Land Rover. A former owner saw the blog by chance, recognized their old Land Rover, and got in touch. Eventually this person could give me all the information they had, which included a DVLA history up to their ownership and all the repairs and mainenance they undertook.