Just spoke to a mate at DVLA. Unfortunately, car registrations were dealt with by local authorities and only transferred to DVLA in 1983/84. Anything prior to that would have been put on the DVLA computer if still taxed (or if taxed / changed owner since then) but that one hasn't. She did confirm that it was registered in London between 1903 and 1905 though, and given RDS' commnets above, that does suggest 1903.