Two layovers in China (but under 24 hours)

No, you do not need a visa because you have right to transit in this way in the case if your total transit time, counted from the time of landing into Guangzhou until your departure from Beijing, is shorter than 24 hours. In other words, you will be covered by 24 hour visa free transit scheme.

Now, since you will have only 2 hours of layover in Guangzhou, you will really have to run. The very first detail upon your landing in Guangzhou is that you run to transit counter (desk) where you will apply for a temporary entry permit. This is free of charge and here you will present your flight tickets. In order to speed up this formality, I strongly advise you to pint out your flight tickets and to have them at hand in a hard copy. After a very short check, you will be granted a permit, then you will run to immigration because your next flight is a domestic one and then run through security and to the gate of your flight for Beijing. Having two hours for this transfer is a very tight time and I hope you are traveling on a single (through) ticket where the luggage is tagged all the way to London. You have a bit better situation at PKX airport though... In any case, just be fast and formally you really do not need any kind of visa.