Probably a blocked fuel line filter. Find the filter and then clean it.
Richard Oldroyd, October 2014
I don't know your engine but I've had several old technology cars over the years and have had a problem like yours more than once - does not neccessarily mean it's the same solution but...
The diaphragm in the petrol pump can become perished and not work as well as it should - sufficient fuel for starting and slow running might be delivered to the carb but when the demand increases the poor old pump isn't able to keep the fuel flow up - the engine (float chamber) becomes completely starved of fuel until the pump can catch up and then off you can go again.
You used to be able to buy petrol pump repair kits - gaskets and diaphragm included.
