Although in general I'd advocate wired systems, in some situations it's not really practical. I'd not fancy trying to run wires across 3 floors, with poor or no access to the necessary void spaces. So I'd probably go with wireless interlinked in this situation.
I'd be looking as a minimum at one smoke detector in each hallway / landing, and a heat detector in the kitchen.
It's normal practice to use heat detectors in kitchens rather than a smoke detector, to avoid false alarms from normal cooking.
I don't have any particular advice re brands, I'll let others comment on that. I can't imagine there's much wrong with whatever screwfix are selling.
Your thread title also mentions intruder alarms. These are nothing to do with fire detection systems, and not interconnected. This would be a different system. Seems this is a thing.