I watch gardeners world now and again and yes, they occasionally have guest gardens on, and there have been several of these tropical gardens you speak of. I love the tropical plants. It's a good job we don't have a conservatory because I would fill it with those type of plants.Your palm looks like trachycharpis fortuni, spelling is probably wrong from memory. These are one of the hardiest palms you can get for the UK.
They can suffer when small so I would add fleece and straw in the winter. Once they hit about 4 foot they become a lot tougher. Should survive uk winters OK.
I'm also a keen gardener and grow palms, bananas and tree ferns amongst others. With a little work and research it's amazing how tropical you can make a UK garden look.
Fish keeping and gardening are great hobbies and the two can become intertwined. I fertilise my plants with dirty pond and tank filter water and collect leaves, fronds and botanical from my garden for my tanks. Also have a turtle pond in the garden so both hobbies are very much linked.