[Mondial]

Arran, a lot depends on the series resistance of the power transformer secondary winding. 

The main limitation of the rectifier tube is its repetitive  peak current rating. As you increase the capacitance of the first filter, the rectifier conducts a higher peak current for a shorter portion of the AC cycle waveform. If the transformer winding series resistance is very low this peak current can exceed the tube's maximum rating. In this instance, the rectifier only conducts at the very peak of the AC waveform and the DC output approaches the peak AC voltage (1.41 Vrms)

If the transformer has a high winding resistance, then the size of the cap doesn't make much difference because the rectifier peak current is limited by the series resistance.  Under load, the cap voltage never reaches the peak AC voltage and conducts for a greater portion of the cycle, resulting in a lower DC output voltage. With a larger first filter capacitance the DC output voltage will not change much, but the ripple voltage will be reduced.