If you don’t want your device to allocate or store passwords, for whatever reason, I’d recommend this.
Pick an uncommon two part word. Convert the obvious letters to numbers (eg 6 for b, 1 for l, 0 for o).
Split the word and put the first three letters of the website name in the middle. Use this for everything. Choose a special character to finish off with, always use the same one.
Then, for instance, if you use rainhood as your word and @ as your special character, your password for GN would be Ra1ngrah00d@, Ra1nmarh00d@ for M & S .
Sounds complicated, but it’s soon second nature, and you’ve no need to write anything down.