Demolition and the planning system interact in a convoluted way.
Basically, planning permission is required for most works of demolition, but the right to demolish is granted in advance by standing legislation, unless that has been withdrawn in your particular case. In any event, you have to give the council notice of the demolition work so that they can approve the method. Whilst they are thinking about that, they may also attempt to withdraw your rights to demolish if it's appropriate to do so. It can get very fiddly, and usually only good for the lawyers.
It doesn't come up very often. Usually you include the demolition you want to do as part of your overall planning application for the replacement structure, as happened with the Main Stand and the Wooderson Close houses. That avoids all the potential mucking around involved in gradual demolition by stealth. The downside is that the whole project, including the demolition, gets assessed against planning policy, which doesn't like the loss of housing. Not insurmountable, but a significant complication. Ultimately, planning is about weighing the pros and cons, and the loss of the houses would be assessed in the context of wider economic benefits associated with the scheme. Based on the main stand project, Croydon council seems very supportive of redevelopment at selhurst, so it could be done. I would expect replacement housing elsewhere as an absolute minimum, though.
That's just to get planning permission. To actually demolish the houses the club would, of course, need to own them. One route is to buy them one at a time as and when they come on the market. Not unheard of. Usually done on the quiet. Or, the club could make overly generous offers for the houses and see if that works. Usually done if the project has become imminent rather than theoretical. Or, the club could ask the council to use a Compulsory Purchase Order (CPO) to buy the houses by force at market rates. That can only be done if essential for a specific public benefit. Redevelopment of selhurst might be such a benefit, though possibly not so great as to justify such a draconian CPO. It would be very different to, for instance, using CPO to get the slither of carpark from Sainsbury's for the main stand. That would have been an open and shut case if it had got as far as a CPO.
Liverpool did a mix of all three for their stand project I believe. I'm not sure that there is the same demand for housing up there, though, as in London and the club has a much more central role in the international image of the city than Palace do, so not really a straight comparison.
Plus, Liverpool were absolute arseholes to their neighbours. They ran the streets down by letting the houses they had bought go to rack and ruin, piling on unfair pressure on those remaining residents who didn't want to sell until they had no choice. They totally shat on a community. The papers touched on it once or twice but soon went back to portraying the club as having a special bond with it's poor but honest working class people, and all that s***.