Landing at Heathrow and making it to Buckingham Palace for tour

Not impossible but it’s not likely to be fun either. You may be scheduled to land at noon but your jet still needs to get to its gate. Then you’ll have to exit the aircraft, collect your luggage, get through Heathrow formalities and then wait for transit to get from Heathrow to Kensington (1-hr) to check-in at your hotel, & drop off your luggage. Then get to Buckingham. All this while jet-lagged and without any time for lunch.

I am going to assume that your plane lands on time. I usually plan for about an hour to deplane, get to passport control, and then grab checked luggage when arriving at Heathrow. There is usually a lot of walking involved. If you don't have checked luggage it can go a bit quicker.

I'd get an advance ticket for the Heathrow Express which will get you to Paddington Station faster than other modes. Then, take a taxi to hotel drop luggage and make your way to your tour.

It is entirely possible to get to your tour by 1600. If this is a high priority item for you, then go for it. If it just something you are mulling about, then choose how much stress you want to put yourself through and if it is worth it to you.

I agree with Kenko. I wrote a very similar reply, but it somehow got lost. It's even a gamble that your flight will arrive on time.

We generally don't book anything in advance for our arrival day. At worst, you would be out £34.

In my opinion, I would go with the attitude of seeing how quickly and/or smoothly the flight, landing, immigration, transport to hotel went and if there’s enough time, bonus, make your way to the Royal Mews. Stressing over a time crunch and having to be somewhere at a specific time after an international flight is not a good way to start a trip.