Most garages now have computerised files, making it easier to piece together a missing history. However, if the original garage has gone out of business or has been bought by another company, records could get lost or deleted in these situations.
First, contact the manufacturer and ask them to tell you what they can about your car using the VIN to identify it (you can find the VIN on your car's door frame or in the engine compartment). They should be able to tell you which dealer originally supplied the vehicle when it was new. You can then approach the dealer and see if they have information on your car.
There is a danger that the car was serviced at more than one garage, and then you won't know who to contact.
A few manufacturers, such as Renault, have centralised records, so if you go into a main dealer they should be able to give you all the service history for that car.
Another possibility is to track down previous owners of the vehicle, to see if they may still have the car's servicing books or know where they took it for servicing. To do this, you need to contact the DVLA (Driver and Vehicle Licensing Agency) by letter.
You need to write to them, quoting your car's registration number and the reason for your request.