As a UK pedestrian and driver, I would add the driver's perspective and norms, to the excellent description of the Highway Code in other answers.
In general, drivers would not be required to stop for a pedestrian other than
- when they have to stop anyway, or are ordered to stop (e.g., traffic lights, police officer, emergency services),
- at a zebra crossing,
- to avoid an actual accident/injury (perhaps due to some careless/unthinking/unaware person, animal or obstruction on the road or appearing to be about to walk on the road, or someone who has clearly already begun to cross the road before the vehicle was present).
Also in general, all road users should act in ways that reduce the chances of accidents. So both drivers and pedestrians should be watchful, and they should not act in ways that force other road-users to take abrupt or emergency avoidance actions to prevent an accident (such as abruptly running into oncoming traffic, or crossing a junction/overtaking where other traffic will have to brake sharply).
Beyond that minimum standard, the social expectation is that pedestrians are expected to be responsible too - they can cross as they like, but should do so in a way that other road users don't have to take emergency avoiding action, and avoid creating a significant risk of an accident. So they should cross where it's more visible, check for traffic, make sure they act in a way that traffic can see and anticipate their intention and actions, and so on.
Within those expectations, a pedestrian can pretty much cross any road anywhere (except a motorway which should be pedestrian-free).
The only other social expectation is that some drivers, and some pedestrians, will be courteous and indicate that the other should go ahead.
But "waving someone on" is a social courtesy only, and the other person (driver or pedestrian) should still check it's safe before doing so, in case there are other pedestrians or oncoming drivers who have not seen them, and an accident would be caused. Therefore as a rule, drivers often do not indicate to pedestrians to cross, in situations where another car driving in a different lane might not see the pedestrian walking out in front of the first car, and hit them. That risk is lower if there is only one lane, however, so in that situation it's more common.