Three bands, printed on the site, and you tell us which one is yours. There is no form, no proof and no conversation about your household beyond what you volunteer. Self-assessment is not a soft option; in nine years it has been abused twice and both times it mattered less than the twenty people it let in.
The arithmetic: the full fee subsidises the other two. The practice holds a fixed number of reduced and lowest-fee places at any time, which is why they run out, and why we print how many are open rather than saying places are available.
If your circumstances change mid-way, in either direction, say so and we move you. Nobody is asked to leave because they moved down a band.