An interesting conundrum!
According to Footman-James Insurance Brokers pre 1966, cars were often made without seat belts. Many manufacturers offered seat belts as extras to the car. Therefore, if you own a classic car and no seat belts are fitted as standard, you have no legal obligation to have them fitted. However you should bare in mind that young children under 3 will not be able to travel in your vehicle.
As to child seats it might be worth talking to these people:
Classic Seat Belts It might be worth having full seat belts fitted to the rear for when the child is over 3.
But for now I'd look for a rearward facing seat that can go on the front passenger seat: even though most are iso-fix there are ones that work with the seat belts as well: the Britax website says "the baby seat can be fitted in to your vehicle by using three different options. The Britax Baby-Safe belted base, the Britax Baby-Safe Isofix base or using your 3 point seat belt system."
So, go to Halfords and try some....