Some clarification . . . don't know where this thing about the diameter being twice the wavelength comes from. Maybe this is a minimum (though I doubt it), certainly not a maximum.
The way I understand it now is that the bigger the dish the better, the more it can receive, the more sensitive it is. ie it can recieve fainter and fainter sources, the larger it is.
Size is also related to resolution, how well the telescope can resolve between objects close to each other. Wavelength / distance = angular resolution. As distance (diameter of dish or distance between 2 seperated telescopes*) increases angular resolution gets smaller (which in this case is good - the smaller the resolution the better).
*Interferometry, using two or more telescopes in tandem at differet locations, increases resolution (but not sensitivity).
The wavelength of 1420 MHz is 21 centimeters, hence the fact that it's also referred to as the 21 cm line.
So the dish needs to be at least 21cm accross, or 42 cm if the double wavelength thing is correct . . . but the bigger it can be the better.