Fitting any sort of thermostat is going to be a problem due to the way your boiler works.
At the moment the boiler is turned on by the HW side of the mechanical timer. That's why you cannot have heating on by itself. In the summer you only need the boiler on as the cylinder is heated by "gravity" circulation. In the winter you also need the pump on to circulate the water through the rads, which happens when you set the timer to Heating and Hot Water.
It would be possible to fit a thermostat to control just the pump, but what you really need is a way of turning the boiler off when the house is up to temperature or the HW cylinder is hot enough, which can happen before the boiler stat turns the boiler off. You will need extra components to do this, but it will save on your gas bill as the boiler will only be working when the house or the HW needs heating up.
Your boiler is at least 10 years old, so it's not so efficient as a modern condensing boiler, but there's very little to go wrong and it's likely to last many more years. So updating the controls as suggested above is a sensible thing to do.
There are two ways you can update the controls: (1) convert to a "C Plan"; (2) convert to fully pumped. Option one will cost less, could be done by a competent DIYer, but would save less. Option one is the more expensive as it would need to be done by a heating engineer, but the savings would be greater. When the boiler has to be replaced the system will have to be converted to fully pumped to meed Building Regulations, so option two would be an advantage.