Here is my complete circuit:
View attachment 251022
This was the only solar panel I could find at my local electrical wholesaler. The rating is Vp = 18.36; Ip = 0.54A. I use the voltage regulator to provide a constant 12V to the battery. The inverter then provides 12Vrms to the transformer, which is stepped up to 220Vac on the output. The lamp is a 10W lamp. Would this work out as expected?

I run a company in standby power and we used to use 4047 based circuitry 30+ years ago. We also discovered that a standard filament lamp would shine at the same brightness with 266 volts on the square-wave output and be exactly the same brightness if running from UK mains of 240 volts. Modern LED lamps will not operate on square waves and will treat the waveform as a dimming command and only light up dimly. If you need more assistance please contact me.

 

I run a company in standby power and we used to use 4047 based circuitry 30+ years ago. We also discovered that a standard filament lamp would shine at the same brightness with 266 volts on the square-wave output and be exactly the same brightness if running from UK mains of 240 volts. Modern LED lamps will not operate on square waves and will treat the waveform as a dimming command and only light up dimly. If you need more assistance please contact me.

Modern non-dimmable LED lamps with switched-mode power supplies will run on a squarewave supply.
Non-dimmable LED lamps with a capacitive dropper may fail (due to the pulse currents through the capacitors on the edges of the squarewaves)
Dimmable LED lamps will possibly be fooled into thinking they are on a dimmer (as you said)
If 266V peak gives the same brightness as 240V sinewave that would imply a mark-space of around 90%.
A mark-space of 64% with 325V peak would give equal brightness to a 230V supply, and also give the same peak voltage as the sinewave, so that devices which rectify and smooth the waveform would work correctly.