Scamps are great little trailers, a little rough around the edges (materials and finishes are pretty basic), but functional and easily customizable. We enjoy ours. We don't use it for long-term travel and living, but if I were 21 and unattached again, I might!
"Around the world"... A trailer pretty much confines you to one continent. You could, as others have suggested, buy one here, use it to tour North America, and have it shipped to the UK when you're done.
It won't be cheap. They're in high demand here, so prices are high and availability is limited. You'll have to purchase a tow vehicle, which you'll have to turn around and sell when you return. You'll pay shipping and import fees. Once it gets there you will have to convert the electrical
system to 240V. The door and utility connections will be inconveniently reversed when using campgrounds in the UK. If camping without hookups, Scamp's 12V system is rudimentary and will require additional investment to make it self-sufficient.
I know a person that installed a Cubic Mini woodstove in his 13' Boler
(just like Scamp), and it has worked well for him through three northern winters. However, he has it parked in one place as a semi-permanent home, and fuel wood is readily available locally. It requires a lot of off-season work to prep the wood because it uses such small pieces. For nomadic use, carting a supply around seems impractical (and likely violates local rules intended to prevent introduction of invasive species). Finding good quality, locally sourced fuel wood on the fly could be problematic. Propane
heat is simple and cleaner burning.
Honestly, renting a car and tent camping seems more practical for your world travels. Then look for a small camping trailer in the UK after you're settled into a job. If you're really set on a Scamp, you might be able to rent one for a few days while you're here to test the waters and decide whether it's worth the trouble to import one later.
Best wishes as you formulate your plans! Another maths teacher here! My first year teaching (1984) I lived in a remote location in a Scamp-sized, wood-framed trailer. I visited Edinburgh as a student in 1981. My most vivid recollection was getting stuck in the wee hours of a January night at a small rural train station and spending several hours in an overheated office with the station master whose brogue was thicker than his cigar smoke.