I came across this simple summary of seat belts in classic cars from Footman James.
Until 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 bear in mind that children under 3 years old will not be able to travel in your vehicle. Children over 3 years of age are only allowed to sit in the back seats.