Pretty much from the beginning Roman Brittania seemed like a nightmare: open rebellions, civil wars amongst client kingdoms, tax revolts, supporting of usurper Emperors. This was even before raiders and started being a major problem from the west, north and east.
Three legions permanently billeted and the building and rebuilding of 100s of forts and two walls are a huge expense.
There's also the Legion destroyed by the Silures and the one by Boedicca (and potentially the 9th :p).
My question is why did the empire try to keep the province? Was it the mineral wealth of the west, the fertile south? A prestige thing? Especially in that first 150 years it seemed like it was all expense and no payoff?
The Roman historian Tacitus does mention Britain as a source of gold, silver, and other metals, as well as pearls (though he disparages the quality of the pearls), and that the land is good for growing crops suited to the climate. (Tacitus, Agricola 12) (Tacitus was not necessarily well informed about the realities of the local economy--for instance, archaeologists have found very little evidence for gold mining in the Roman period.)
On the other hand, we don't have an accurate enough sense of Roman revenues and expenses to say whether Britain was profitable as a province to Rome in the long term. The benefits of the conquest were instead primarily political. The conquest of southern Britain and ongoing operations in the north and west conferred prestige on the emperors who directed them, furnished lucrative commands for favored supporters, and provided opportunities for plunder and slave-taking to keep restless soldiers happy. Considering what tended to happen to unpopular emperors who didn't have loyal followers and soldiers willing to fight for them, Britain may have seemed like a bargain, no matter what the revenue flows were like.