The only one I'd definitely pre book on that list Is the Churchill/Cabinet War Rooms, they introduced timed entrance slots, its become very popular, this is the best way of managing the queues.
If you start paying out now unnecessarily and your plans or flight changes, or your jet lagged on the day, you've likely lost your money.
Parliament for myself was no charge, I arranged this through my Member of Parliament, but this is a popular tour so monitor this.
For HCP there is no advantage buying train tickets ahead, this is a 35 minute commuter run from Waterloo station, about 2 direct trains per hour, buy on the day, check out 241. See how you're days are looking and how you feel, check the weather forecast for HCP and as mentioned any other events on site. I'm over 2 hours by train from HCP, I'll decide my visit the night before and won't pre purchase anything.
Warner Bros studio, if that is in your mind, definitely Pre book your slot, go DIY, don't use a tour company.