It is a logistical nightmare to do it by anything other than age (as has already been proven with the “healthcare”) category.
The system to ensure that everyone (who wants to be) gets vaccinated and everyone only gets their two doses (no trying to get different brands) is tied to NHS numbers. Age is also tied to NHS number, along with sufficient medical information to categories people by clinical vulnerability. Occupation is not listed against NHS number. This means that if occupation based categories are opened, it will be very difficult to work out who is eligible to book. There will be no way of restricting the booking system on occupation grounds that would not require significant changes in the set up.
The nature of Covid, and need for social distancing, means that you can’t have, say, a”teachers day” at a mass vaccination centre and allow all teachers to simply turn up. There needs to be a way to control who turns up when. What would happen if open booking was allowed is that people would book who aren’t in that category - either because they really want the vaccine, or they don’t understand the system or anything in between. The process of proving eligibility etc will simply slow things down.
I really think - as deserving as frontline police, teachers etc are - it is likely to be faster (particularly with how well we are doing with it) and more effective in the long term to simply keep firing through in age order. The time and resources required to do anything else will have such marginal gains in improving the efficacy of the vaccination programme, that I suspect it simply won’t be worthwhile to organise.
Of course this opinion may not be popular. But public health is about whole populations, not individual people. We need to look at the best overall strategy for the population, not individuals within it.