You must not be a good guesser, as both are wrong.
Problem still exists, possibly you did not read the results in post 11, no further experiments proposed or items to check with the instruments I have, and the thread got side tracked talking about the various types of 4 foot LED lights.
Not 'side tracked', your issue is most likely that you're using unsuitable lights - which aren't regulated, so they flicker as your mains varies. However, while using better lights should cure your symptoms, the main issue is probably why your mains is varying just from a washing machine?.
My house has very old incoming electricity cables, so far thinner than modern requirements - I think they are only 6mm?, modern requirements are 10mm? - so when the shower is turned on the lights in the master bedroom (which are dimmable LED's on a dimmer) dim CONSIDERABLY. I think this is exaggerated by the LED bulbs been too big really, so they run at a pretty low dimmer level in normal use.
None of the other lights in the house, all of which are regulated LED bulbs and tubes, are affected at all. Many of the bulbs are Philips Hue controlled by Alexa, and I've been considering altering the master bedroom lights as well.