Timings for layovers

You are correct when you say that such an itinerary is eligible for 24 hour visa free transit. You do not need any kind of visa because your entire transit time within mainland China is shorter than 24 hours.

As far as your fear of not being able to catch your following flights, the most important detail is, if your booking is on a single ticket and if your luggage is tagged all the way to your final destination in London? If this is the case, then you have enough time to perform this itinerary. However, if you need to collect your luggage and then perform new check-in, then that would not be doable because of too high risk of losing the flight.

So, if your itinerary/journey is under the same ticket, you can proceed. Important detail is that the first thing you will do when you land in Guangzhou is to approach transit counter where you will apply for a temporary entry permit to be allowed to cross the immigration because your next flight to Beijing is a domestic one. Here you are advised to print out your flight tickets and to have them at hand, ready to be presented to relevant authorities. By the way, this application is free of any charge. Upon your landing in Beijing, you will cross the immigration and proceed to the gate for your flight to London.