UK to Beijing 72 hour exemption?

Victoria, you are definitely eligible for 144 hour visa free transit in wider Beijing area and you do not need any kind of visa. It is important to emphasize that in Beijing there is only 144 and not 72 hour visa free transit. Many years ago 72 hour was replaced by more generous 144 hour visa free transit.

Also, it is essential to emphasize that you can use 144 hour visa free transit only if you have just one stop in Beijing or in other words, your itinerary cannot look like:

London - Beijing - Shanghai - Manila

but only

London - Beijing - Manila

As far as your return flight is concerned here you will be covered by 24 hour visa free transit and you do not need any kind of visa. When we talk about 24 hour visa free transit it is usually understood that the passengers will remain airside (within the transit area), but when the layovers are longer as it is yours, then the officials usually offer a temporary entry permit, allowing you to exit the airport. In any case, upon your landing in Chengdu, the first thing that you will do is to approach 24/144 hour visa free transit in the same way as you will do in Beijing, where you will apply for a temporary entry permit by presenting your flight tickets. Your chances to be granted a permit are very good and hopefully you will be granted one. When you are done with this step, you will head to the immigration and then to the city to enjoy some time on your own. Have a nice journey.

Amazing, you have made this so clear for me. Thank you very much