With my first car (r5

) there was loads of sediment in the petrol tank.
When you let petrol get low, this can clog up the fuel lines, sometimes if I went to accelerate, it would push the sediment through and either judder and cut out or judder, pause for a second then be on its way.
Try changing the fuel filter, fill the tank with petrol and put a shot of redex in when filling up, and try not to let the fuel gauge reach the red.