A car with a blocked fuel filter may run fine on flat ground and on downhills but as soon as you look at a hill it will start to hesitate.
To check if the car is out of fuel, undo the 3 screws on the top of the float bowl on the carby, remove the top and the bowl should be about half full.
If you want to see it you have a fuel blockage or if you want to check that the fuel pump works, take the hose off the top of the float bowl and stick the hose into a clean bottle (600ml coke bottle will do) If you have an electric fuel pump turn the key on and it should start to pump fuel into the bottle. If you have a mechanical pump you need to wind the motor over on the starter and it should start to pump.
If the pump is not working and you need to move the car you can tip fuel into the float bowl (after removing the top) and you can drive for about 30 seconds.