Sidenote: in LTspice, the amplitude for the sine source is actually the PEAK amplitude, not the RMS value transformer ratings are in. So V2 is putting out 17Vpk, or 34Vpp.
Do you have a particular simulation model for those polarized electrolytic capacitor symbols there? I use the stock symbol you get when you press C on the keyboard, or click the capacitor symbol in the toolbar. I'm starting to wonder if those are actually working as the capacitors they're intended to be, within the simulation...
Just slapped together this quick sim, and works fine with the floating voltage source.
So the heater winding of your transformer is supposed to put out 6.3V AC? That would translate to an 8.8V amplitude for the LTspice sine source. And didn't the UK run on 50Hz mains?
Later edit: 2nd attached screenshot also contains an LM317 with some eyeballed adjustment resistors, putting out about 6.5V (blue trace; white trace is LM317 input voltage).
No idea what exactly is or isn't going on in your sim... Do you have 17V set also as a DC offset for V2? Labels are overlapping with the 1N4007 of D7...