Answered by ZUPAN | Nov. 24, 2019 03:40
No, you both of you don't need any kind of visa because your itinerary is eligible for 24 hour visa free transit.
You will print out your flight tickets and have those printouts with you. Also, you will declare at check-in in, I assume UK, that you will travel to Indonesia via Beijing using 24 hour visa free transit. After a short inspection of your tickets, you will be allowed to board the plane.
Upon your arrival in Beijing, you will apply for a temporary entry permit at 24 hour visa free transit counter to be allowed to exit the airport ant to make a short exploration of the city. Anyway, you should be aware that the issuing of a temporary entry permit is always upon discretion of immigration authorities on a day of arrival.