[Arran]

That's because your portable uses battery tubes which are between 1.5 and 3 volts each and as Steve said they are directly heated which means that unlike most AC type tubes there is no cathode over the filament that needs to heat up first. The reason I say most AC tubes and not all is that many rectifiers are directly heated, if you look at a 5Y4, 5Y3 or a type 80 tube they are almost instant on as well. Also your portable likely uses a selenium rectifier which is also instant on, it's an early form of solid state rectifier.
Regards
Arran