I can get Radio Scotland during the day, though the signal is quite weak. I suppose that would be ground wave. The same goes for RTE (Radio Telefis Eireann). At night there is sometimes interference from foreign stations on the same channels as JohnInKansas describes.
   If the radio is a portable one with a ferrite rod antenna, sometimes it's possible to boost the wanted signal and cancel the unwanted one by placing the radio next to a vertical conductor such as a water pipe. Of course, the signals have to come from opposite directions for this to work.

What I should have pointed out before is that when using silicon rectifiers in a circuit designed for tubes, it is necessary to put some series resistance between the rectifiers and the smoothing capacitor. Otherwise when the supply is connected there will be a huge surge of current which could destroy the rectifiers. The 1N4000 series can take a 50A surge for 1 cycle of 50Hz. if the power transformer gives 250v r.m.s. output, the peak voltage will be around 350. Therefore a resistance of 350/50 = 7 ohms is needed. To be on the safe side I'd double it, which would give 14 ohms, and use the nearest preferred value, 15 ohms.
   The problem doesn't arise with valve (tube) rectifiers because the current builds up slowly as the tube warms up. Consequently a valve radio (or amplifier) should not be turned off and immediately turned back on again as there will be a current surge which will shorten the life of the rectifier.