As others have said, it varies borough to borough and there are 32 of them, and Royal Parks have different rules, so you need to keep your wits about you.
Some allow free parking in Residents’ Bays, others don’t. Further complicated by some allowing residents’ bikes to park in Residents’ Bays for an annual fee (eg Camden) but you won’t know if you see a bike there because it is all online now. So for example in Camden don’t be tempted to park alongside because you see another bike, it might have an annual permit.
You have to know which borough you are travelling to and do your research first.
Information is hard to find. For example the Royal Parks allow free parking for up to two hours - although this is not signed anywhere, not on the roadside signage nor on the pay-and-display machine. I know this because I asked an enforcement officer. Of course that was some time ago and they might have changed their rules.
There was a time if you parked on private property, for example a strip of footway which clearly belongs to a shop, you would be okay (assuming the shopkeeper wasn’t upset) but they changed the rules a long time ago to mean if pedestrians have unencumbered access to that area normally, then you can’t park there. You will see some premises owners use bollards or temporary posts and ribbon to demarcate their demise, and prevent pedestrians having full access, for this reason. I discovered this to my cost many years ago and haven’t repeated that mistake.