Please be aware that if you want to use your fire TV stick away from home but still in the UK, you need to take the fire TV remote with you. You can't just use the Fire TV remote tv app on your smartphone.
This is because the smartphone app needs the local wifi signal to operate and when you do that it is no longer paired to the fire tv stick.... The fire TV itself also needs to have its network reset and you can't then do that with the smartphone app because they won't pair.
(Next time I'm away, I'll try getting the fire TV stick to forget the network before I leave home, then I'll see if that works.)
But I found that even with the controller I had to reset the network.
I overcome the mobile problem with having apps on mine and my wife's phone mine set to my home WiFi set up and my wife's set to my daughters WiFi set up. The phone automatically logs into my dayghters WiFi as it is a BT hot spot and the BT app automatically connects.