British tanks in early WW2 were carryovers from the inter-war period, and were a product of fighting the last war, they were invisioned to fight in a ww1 trench-style environment, and suffered from these assumptions. The tanks were generally divided into two branches, Cavalry/Fast "cruiser" tanks, and Infantry tanks:

Cruisers were romanticized a bit and were intended to operate much like their namesake, naval cruisers, these tanks were supposed to be fast, mobile, and capable of flanking and exploitation maneuvers, and eschewed armor, and turret ring size (limiting gun caliber) for suspension and mobility. In the african theater, tanks like the crusader did quite well in the first year or so, using a OQF 6Pdr gun they were a match for the early PzIV German tanks, let alone the PzIII, however they quickly became obsolete as the Germans moved from Pak 36 (3.7cm) to Pak 38 (5cm) AT guns, and eventually the first Tiger I tanks being deployed in Tunisia, as well as the eventual replacement of the "light" AT guns with Pak 40 (7.5cm) guns. On top of them being under-armored, they were not terribly reliable tanks, which turned out to be a major issue in the desert, were the dry, sandy environment (in some areas, not all of north africa is "desert") causes havoc on suspensions, tracks, engines, etc.

Most of the cruiser tanks in North Africa were replaced by m3 Grant/Lee tanks, which although had their own major issues, mounted good armor, a good main gun, a decent AT gun, and overall better reliability than the cruiser tanks, with only some practical loss in mobility (the though of a cruiser tank being a fast riding exploitation tank really was limited more than anything by terrain, unlike its oceanic counterpart, a tank of the time could not move at speed through rough terrain reliably, let alone engage targets while doing so, this greatly limited the advantage of speed outside of particular hard-packed soil/sand areas that were wide open). The M3 tanks greater armor largely negated the 3.7 and 5cm German AT and KWK guns, and were largely impervious to anything the Italians had, falling only prey to the Tiger, FlaK 88, and newer 7.6cm guns. The M4 Sherman just added to the superiority of the Lee, rendering existing British cruiser tanks obsolete.

Throughout the war in the North African theater, development did continue on various cruiser designs, eventually culminating in likely the best pure "British" tanks of the war, The Cromwell, and its asociated spin-offs, the Centaur, Challenger, and evolutionary the Comet. The Cromwell and its family of variants all generally followed Cruiser tank design philosophy, being faster than normal medium tanks, but made far fewer compromises in armor, having armor roughly analogous to its medium tank contemporaries, and now mounting a far more reliable suspension and engine. The Cromwell tank line accounted quite well for itself in northern Europe, with the Up-gunned Challenger version, mounting a 17pdr being a fearsome opponent, and the eventual Comet tank being one of the best balanced tanks of the war, Sadly, these tanks are relatively poorly known due to low production numbers, and deployments that focused on "cavalry" and recon roles in British armored divisions, leaving most of the heavy work to M4 Sherman and Firefly tanks.

Infantry tanks (or "I" tanks) on the other hand were the slow dreadnought battleships of the war (by British doctrine), slow, heavily armored, and armed to support infantry on foot, the infantry tank was almost the polar opposite of the cruiser in design and tactical deployment. "I" tanks in North Africa were also designs that started off in the inter-war period, and those that deployed were at first the Matilda I and II and the Valentine Tank, the major flaws of these tanks were limited mobility (initially they were designed to "walk" at the speed of the infantry), and poor weaponry that quickly became obsolete as the war progressed. They started off with OQF 2pdr guns, which were adequate for their time, but with the rapid tank development happening through the war, this quickly become obsolete, and problematic, as these 'I" tanks initially had very limited turret rings, limiting what guns could be placed on the tank, and by the time this was fixed through re-design, new tanks were in service from american sources, and new designs were coming up the pipe that could handle bigger guns. Later in the war, the main British "I" tank was the Churchill, taking the "I" tank concept even further, it was a large, very heavy, very well armored tank, but still suffered from being slow and having a moderate gun (75mm, same as a Sherman, although a different actual gun, it too started with a 2cm gun), overall the Churchill was a relatively successful tank, and is relatively well known for all of its variants, being the base of many of the "funnies", specialist assault/support tanks, mounting spigot mortars, flamethrowers, bridging units, etc. No real infantry style tanks were developed to completion after the Churchill, with balanced "main" battle tanks (MBT) becoming the norm after the war.

At the end of the day, limiting tanks for armor/speed/firepower, etc for an intended role did cause major issues, and greatly limited the flexibility of these tanks in the field, most of these designs eventually mutated to be more general purpose (cromwell), or were relegated to support/breakthrough roles (Churhill) in favor of more general purpose tanks like the m4.

The British did use tanks quite a bit. The had all the element of tank warfare any other nation had, not quite as advanced as germanys maybe.

J. F. C. Fuller and B. H. Liddell Hart were advocates of the tank. With Percy Hobart the British had probably the most unique tank advocate, and the later used this to great effect.

What the British accomplished in North Africa was considerable, even if you take into account that they were fighting Italians. They showed create skill in war of movement and used this effectively.

In terms of tank design the British were not behind the others. The Matilda II was one of the best in its time. They design many others, Valentine, Churchill Cromwell, Comet and more. They were not always the best but they were not completely useless.

With the Centurion the British achieved one of the best designs during all of the war and its still in use today.

The British also used many M4 Sherman, both in North Africa and Europe. The produced there own up gunned version of the M4 called the Sherman Firefly. This had a very much improved gun and was able to take anything that the germans could on the field. The often combined up gunned Fireflys with the older 75mm Sherman into units.

A honourable mention for the Hobart's Funnies. Percy Hobart was not allowed to fight with the divisions he trained because he was to ill, but he got a job that made up for it. He was asked to design special vehicles, something that he had wanted for some time. These special vehicles gave good account of them selfs. The idea he produced are still used today.

I have heard credible historians say that the British relied TO MUCH on tanks, but I am not sure if I agree. However it does show that the British were very much into tanks.

I think the problem arises from the fact that in English writing, American output is far greater, and focuses on americans. When the Brits are mentioned is usually connected with strategy, the navy or the air force. Americans somehow feel that the Overlord was their show because the wicked brits had wanted to stop them and redeploy them to fight in Balkans or something.