I flew from Washington DC to Devon (UK) roughly 9 hours ago.
My MacBook knows that I am in the UK, but won't update the timezone.
How do I make sure that the MacBook keeps updating the time zone automatically?
I assume you 'unlocked' the pref pane with the icon at the bottom left.
You could try using the Terminal command
sudo ntpdate -u time.euro.apple.com.
If the command returns errors such as
Can't find host or
no servers can be used, the network you're connecting to might have a firewall block on ntp servers.