As far as "properly themed" goes, yes, Chessington is the "template park".
However, I don't think Tussauds would have invested in Chessington if Alton hadn't kickstarted the whole "Theme Park" thing. I can't find when they actually started calling themselves a "Theme Park" and I suspect it was probably post John Broome (so Tussauds).
However, if you look at Alton in the mid-80's, you could easily argue it was a "Theme Park". The area around the courtyard (Cloud Cuckoo Land and the now closed off Coaster Corner) had individually themed rides (things like Doom and Sons and Around the World in 80 Days). The Dinosaur area was themed too.
It's things like naming specific areas of the park though and creating a general theme in them that makes it like a modern Theme Park. If places like Kings Dominion today can class themselves as a "Theme Park", then Alton in the mid-80's absolutely could.
The basic blue-print was there and it was successful. It took several years for other attractions (such as Chessington, Drayton Manor, American Adventure, etc) to catch on that there was money to be made from a "leisure Park (to use Alton's terminology) after the disaster of in-land parks in the 70's. While everywhere else was closing, Alton was booming, and doing it by presenting not a "seaside park inland", but as a new kind of park, stolen right from the booming American Parks.
Actually, I'd argue Camelot was the first UK "Theme Park". They had Arthurian animatronics, rides named after famous Arthurian legends and a complete park "theme" very early. Though when I went in 1982 or so, I couldn't quite work out why they had a cowboy stunt show and American styled miniature railway :lol:
But yeah - we'll ignore that
![Wink ;) ;)](https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f609.png)
Alton created the "market", but Chessington was the first park to
really take the Theme Park concept and run with it in the UK.