If you have the option try a different UK server - they can get busy - especially the default ones and that causes buffering.
Obviously make sure your internet isn’t the factor.
The giveaway is that if I watch something else, like France 24, which isn’t routed via the VPN, the stream is very steady. We have 500mb fibre here now and a three node mesh WiFi setup. I’m running two Fire TV sticks, one on the TV in the kitchen and one on the TV in the lounge, and they both exhibit the same symptoms. They are well in range of the WiFi and getting hundreds of megabits of steady WiFi signal. While I can toggle the VPN to change the IP address, I can’t change the actual server that easily, if at all - Cyberghost provide choices for optimised for iplayer, Netflix, etc. If I choose a plain UK server, iPlayer doesn’t work. It may be I have the best of what I can expect but I need to verify that, so I will try the ExpressVPN trial alongside Cyberghost.
Just out of interest has anybody got an alternative to the ghastly Silk on Firestick?