Areas near airports would be fast to reach, but onward travel from the airports wouldn't be so much faster than 100 years ago.

And the oceans would look different - it still takes a long time to reach the mid-atlantic!

London to anywhere in Europe in <4 hours, so that's the 5-days bubble.

North America was then clearly the best connected part of the world from London, this is probably still true - today New York is 6-7 hours, San Francisco ~11. Honolulu can be done in just over 20 hours.

Central Africa is obviously immensely better connected today, due to aviation. I'm pretty sure you can get to any airport served by commercial, scheduled air traffic in Africa in <20 hours, and any airstrip in Africa in the same timeframe if you're willing to charter a plane.

India is <10 hours for Mumbai, Delhi and Bangalore and Kolkata is reachable in a few more hours connecting from there. All of India is extremely well connected by domestic flights, so <20 hours should hold up fine.

For South America, Rio de Janeiro and Buenos Aires is 12 and 14 hours respectively and in Australia, Perth, Melbourne and Sydney are all reachable in <24 hours.