Stop Over - Are we eligible for TWOV?

The first thing is that the Spanish passport holder can enter and stay in China absolutely visa free for up to 15 days, so she/he does not bother about this TWOV stuff at all.

UK passport holder will use 24 or 144 hour visa free transit schemes because the itinerary you have presented is definitely and undeniably eligible for both visa free transit options. Which one will a UK citizen use depends on the length of the layover in both Guangzhou and Beijing. If the layover is shorter than 24 hours, it will be 24 hour visa free transit and if it is longer than 24 hours, it will be 144 hour visa free transit. In both cases, no visa is needed.

So, UK passport holder is definitely eligible for both 24 or 144 hour visa free transit and the Spanish passport holder travels absolutely visa free. Both of you, have a nice journey.