Just run some numbers. By mid September 6.5m people in England had received a positive test result at some point in the pandemic. This is the group who could potentially get a reinfection during January and it's 11.5% of the population of England (56.5m). Boys3's calculation is that 12.35% of cases in January were reinfections, meaning that those who had a confirmed infection by September were slightly more likely than other people to report a new infection during January.
Obviously a whole load of confounding factors here - some people more susceptible due to lifestyle, biology, etc. Some more likely to report a case. Vaccination status, etc. But does point to Omicron being very good indeed at evading immunity from past infection.