[Engine] Fuel problems when the tank runs low

[Kez]

I kinda have an idea what this anyway, but thought I'd ask in case I'm wrong.
I have a 1.9 non turbo (trying to work out what engine code it is), it runs fine when there's between 1/4 and a full tank, but once it gets lower than 1/4 it coughs and splutters every now and then like it's running out of fuel. If I keep going, the lower the fuel gets the worse it becomes. I got to the top of the red marker and the engine cut out and wouldn't restart.
I put a big can of diesel in and eventually it ran, but stopped again.. in the end I got it to keep going and it's fine providing i keep to more than 1/4 of a tank.

I'm suspecting the pickup pump? What do you think? Is this a known problem?