If you are wanting to find out the History of your pre 1969 Mini there is only one place to start, Thats British Motor Heritage, although they have been "put through the wringer" over the last year or two since the shake-up and near demise of Rover group. They are however still going strong and if you follow the link below you will find their most informative website that will tell you more than I ever could.
Heritage Certificates
If you are wanting a heritage certificate for your pre 1969 (the records stop in 1969) Mini & don't want to wade
through the entire BMIHT site. Follow this link.
DVLA
If you are the legal owner of your car, the DVLA (Driver & Vehicle Licencing Authourity) will be able to
supply photocopies of all the logbooks of your car since new. Very usefull!