I think we are going to have a bit of a problem with terminology, as the British seem to speak a different language, than we do!
I don't know what you are referring to when you speak of cellulose paint. In the distant past, we had a lacquer paint that was called nitrocellulose, but it hasn't been used on "new" cars since the late 50's. It was surpassed by acrylic lacquer, which held up better.
But nitro is VERY hard to find any more, available only through specialized antique dealers. Even acrylic lacquer had been banned in may areas and getting hard to find.
So, hopefully to answer your question, if the car is about 15 years old, never repainted, and is 2 stage (color+clear) most likely it is a modern urethane system. Good news is, that paint is pretty easy to paint over with no problems. I believe whatever paint you buy will probably be a modern style paint, base, clear, which should be compatible. Just be sure to use a good sealer right before you put your color on it.
Just a note...in the US, we have 2 different systems of paint, lacquer and enamel. Lacquer is air dry and has been explained.
Enamels are broken up into categories depending on chemistry. The first enamels were called synthetic (DUpont-Dulux)....air dry, slow to dry and stay soft for a long time, still available as a cheap paint.
Next came acrylic enamels (Dupont Centari) faster drying, still air dry, and more durable. Later, they sold a hardener for it that made it even tougher, glossier, and used chemistry to make the paint HARDEN instead of air dry. The hardeners were also pretty toxic, so you had to wear a charcoal filter to be safe.
The next step was urethanes, ( Dupont Chroma-one, and Chroma-base paints) now completely hardening paint, no option for air dry. VERY hard and durable. High gloss, chemically resistant, and good abrasion resistance. This is what we use today. There are also versions called polyurethane (available in the past, as Imron) that are very similar in chemistry, and also very tough and glossy. Mostly used as industrial paint, and for trucks, buses, and planes. The finishes are not as glamorous as the modern urethane base/clears.