To drive an ATV quad bike on the road one needs to have a full car licence. An ATV quad bike can only carry passengers if it is designed to do so and has the right number of seats.
a four wheeler has four wheels and is called a quad. its more safer riding a quad than a dirt bike. a dirt bike has two wheels. it's much lighter then a quad. so its easier to do tricks.
There are a number of places where one might be able to purchase a Suzuki quad bike. They can be purchased at most motorcycle or dirt bike stores. They can also be purchased used on websites such as Craigslist.
Tom Cruises character rode a Triumph Speed Triple (an urban bike with a 1L engine) and I believe that the bike riden by Dougray Scott was a Triumph TT600 (a sports bike with a 600cc engine)
The short answer is no, if you only have a cbt you are restricted to 125cc with L plates. The 33hp limit applys if you take and pass your full test on a 125cc bike, after 2 years it automatically becomes an unlimited licence.