Well, first, pre-Roman Britain wasn't so undeveloped as it may seem. Remember, our primary written sources about Britons are Romans, who were really xenophobic and dismissive of other people's cultures. But, due to contact with Rome, Briton kings minted coins, adopted some elements of Roman culture and tradition, and developed trade with the continent. It wasn't Alexandria, but it wasn't a wasteland as well. All land has some riches if you're willing to look for them. After all, it was 1st century AD, and if nothing material could be pillaged, you could always turn humans into property via slavery.

So, with that out of the way now:

Rome had, since Augustus, a bunch of client kings in today's Southwest England. What a ''client king'' means varies from case to case, but usually it's a sort of alliance with Rome where Romans are the senior partner. They are not a part of the Empire, they don't have the same obligations as citizens do, but they are obliged to provide some soldiers if need arises. In return, Rome gives the kings assurances that his/her lands will be secure from foreign invaders. In fact, usually when Romans were conquering territory, it was on the pretext of Tribe B attacking a Tribe A, who is, what a coincidence, a Roman ally as well.

Now, to understand hows and whys of Roman conquest of Britain we need to look at Augustus' policy regarding expansion. Very early in his solitary reign, he realized that the current state of affairs was unstable. He realized that there is too many soldiers, who require money, which requires taxes, which come from Italy and other provinces bled dry by three decades of war. He reduced the army to a bare minimum- as soon after Augustus died, two army rebellions broke out in Pannonia and Germania because he was overworking and cutting pay for those remaining- and laid a plan for the protection of the Empire: to the East, we make peace with the Parthians and have our clients in Armenia. To the West, we have ocean (which means that Britain is a no-go). He tried, and due to Roman defeat at Teutoburg forest, failed, to reach Elbe. He had to settle for the Rhine as the border, and he also reached Danube to protect Pannonia and Illyricum. Furthermore, he was a great diplomat as well. At the time Augustus died, all around the Rome's borders were allied nations. Even the Parthians, their only serious contender to the East, had several shah's who were quite openly placed there by the Romans. Same goes for Britain. At the time, Rome was content to have loyal client kings across the Channel, and that was it.

Now, Augustus died in 14. AD. His reign, as well as those of Tiberius and Caligula, on foreign fronts went quite peacefully. That was the famous Pax Romana. It changed a bit when Claudius came to power. He was, as tradition goes, placed by Praetorians as Emperor because he was the first one from the imperial family whom the Praetorians saw, hiding behind the curtain. It was widely thought that he was mentally deficient (which was strange, considering how he was quite a capable administrator, not to mention a great scholar as well, but I digress), and you could say that, within the hornet's nest that was the Julio-Claudian dynasty, he was seen as a joke, someone who presented no harm, which was probably the reason why Caligula never bothered with him. Anyway, he comes to power, this joke who suddenly became the Emperor, and now he has to prove somehow he's worthy of his predecessors. In other words, he needs a big victory.

So, when a client king, Cunobeline, was overthrown by his two sons, Caratacus and Togodumnus, what better opportunity was there than to conquer the first territory for Rome since Germanicus' famous failed campaign 25 years earlier? Would you pass an opportunity to do something which even Gaius Julius Caesar himself failed to accomplish? As Romans saw it, peoples inhabiting Britain were fierce and terrible barbarians, who were hiding deep in their woods and sacrificing their enemies to the forest gods (at least that last one seems to be true enough). So, in 43. AD Claudius sent four legions under the auspices of Aulus Platius across the Channel. Troops led by Hosidius Geta and Vespasian, the future Emperor, defeated Caratacus at Medway. Britain was, for the time, peaceful, and Claudius arrived only after all the fighting has been done. He entered Camulodunum (Colchester) and declared it a new capital of province Britannia (which at the time extended only to Southeast). Soon afterwards, all the other surrounding tribes came to offer their allegiance, except the Silurii in Wales, who still continued their resistance.

Of course, Claudius engaged in a huge triumph because of this success. Even though Senators hated him because of his women and freedmen, even though he was generally looked on as a weak, undecisive man, he was still Claudius, the man who conquered Britain.

So, there you have it. A couple of economical reasons, but mostly to grant a new Emperor legitimacy and love of the people, as well as to give his soldiers some riches to plunder and land to settle on.