It’s a really simple process to decide to do it - government either call for a referendum or could simply do it via a vote in Parliament if they felt the political will was there and public sentiment was already clear - but they’d probably do a referendum first on something so big.
The bigger problem is creating the alternative and deciding what everyone wants and wants to fund as a replacement.
The easy question is do you want to be a republic rather than a constitutional monarchy?
It’s replacing all the different bits and making the dozens of decisions that come after that vote which is where the real work starts. And working out how to fund the transition.
The government that starts the process needs to be very secure in office, have no other pressing national issues that are more important to deal with, be able to earmark a significant budget, and work out how to create a team (committee, department, bipartisan department?) to work out the funding and decoupling of the monarch’s influence and ‘branding’ across the armed forces, national law, currency, historical archives and crown estates, as well as coming up with a new head of state option with set job parameters, etc.
It’s the work of decades - of course once it’s done it’s doesn’t have to be done again so that’s not necessarily an argument against it but right now it would be a fairly unpopular option for a majority of people - even if that majority isn’t as big as it used to be. So most political parties aren’t going to touch it with a barge pole if they can help it.