Simple maths.
The vaccine has efficacy against infection of around 70% - ie 30% of people fully vaccinated can still catch it. The vaccine has much better efficacy against the illness being bad enough to cause hospitalisation, so while there are many infections, hospitalisations are much, much lower than pre vaccine (when we also had lockdown restrictions).
Also, there are still a lot of people unvaccinated: 20m+ in this country, although many are children. They have no protection other than natural immunity if they have had it.
I would be very interested to see data on the vaccination status of those hospitalised, split by age group. Is this in the public domain?
There's some data here:
Covid-19: How is vaccination affecting hospital admissions and deaths?
An analysis of UK data from the National Immunisation Management Service (NIMS) and the Coronavirus Clinical Information Network (CO-CIN),1 endorsed by the UK Scientific and Advisory Group for Emergencies (SAGE),2 shows that of 40 000 patients with covid-19 who were admitted to hospital between...
www.bmj.com
For example, between the week beginning Monday 16 August 2021 and the week ending Sunday 12 September, the rate of hospital admissions of over 80s was 50.5 per 100 000 in the fully vaccinated and 143.9 per 100 000 in the unvaccinated, while deaths were 45.5 and 145.4 per 100 000, respectively. These trends were seen across the board. For example, for 60-69 year olds the hospital admission rates were 13.5 per 100 000 in the fully vaccinated and 74.3 per 100 000 in the unvaccinated, while deaths were 4.1 and 24.3 per 100 000, respectively.