How far do economic factors explain the rise and fall of the British Empire?
As is usually the case with questions like this, the answer is "somewhat."
The creation and expansion of the British Empire was done partly for economic reasons. For example, the Opium Wars can be seen as part of this expansion and they were almost solely about economics. However, there were also other factors involved. Economics was only tangentially involved in the creation of the penal colony in Australia. Power considerations helped cause the Scramble for Africa.
This applies to the downfall of the Empire as well. The Empire did fall apart partly for economic reasons as Britain was economically weak right after WWII. But the breakup of the Empire was caused even more by political forces. The post-war era was a time when world sentiment was coming to condemn colonialism and empire. This world sentiment was perhaps the most important factor in the breakup of the Empire.