The tank doctrine of the United Kingdom during World War 2 dictated that tanks be used as either infantry tanks or cruiser (cavalry) tanks. Infantry tanks were designed to move up with infantry and as a result they were characterized by their slow speed, heavy armor, and good mobility. Cruiser tanks were designed to act like cavalry and exploit openings in the enemy defense and as a result they were characterized by their high speed and low armor. In World of Tanks, these classifications have been applied to the standard light, medium, and heavy tank model of other nations for simplicity. Nonetheless, the British tank doctrine still applies and results in oddities like heavily armored light tanks (e.g. the Valentine) and very lightly armored and fast medium tanks (e.g. the Cromwell).
Later British tanks focused on the doctrine of a universal tank. Sporting good armor, good mobility, and very high accuracy; universal tanks were designed to replace the heavy and medium tank doctrine with a tank that could do everything. The first successful British universal tank design was the heavy cruiser Centurion (Mk. 2). Its success set the precedent for later British tank designs as well as the concept of the modern main battle tank.
British light tanks were built as combat tanks in their time, so they don't have dedicated scouting tanks (at least so far). At low tiers, the light tanks have somewhat higher top speeds than the mediums, but their maneuverability is almost indistinguishable. The main thing here is since they are light tanks, the game allows them to move without losing half of their camouflage value.
British medium tanks are ponderous and very poorly armored at low tiers. However, they have good guns. Higher tier mediums become fast with quick firing but low damage guns, then finally evolve in to powerful universal tanks, with good mobility, speed, and accuracy.
British heavy tanks start off slow and ponderous, with reasonable guns for their tier. They eventually become incredibly accurate support tanks, better at moving to positions and giving covering fire than engaging head to head. They also get good on the move accuracy and low aim times. Their armour is generally on the weak side.
British Tank Destroyers were added in the 0.8.4 update. Up to tier 4, they are mostly conversions of other tanks into Tank Destroyers, which are fast and lightly armored. However, their gameplay reverses from tier 5 to tier 9, becoming extremely thick skinned, but somewhat unwieldy assault guns with low damage but very fast firing guns. However all these may have a lot of armor, but artillery is still capable of dealing almost max. damage to them when they are hitting them. The tree ends with the agile and extremely powerful FV215b (183), which is essentially a direct fire artillery capable of delivering HE shell levels of damage with T8 HEAT ammunition levels of penetration.