To cut down, can mean to fell, as in cutting down a tree, but it can also mean to reduce, and in the recession lots of people are having to cut down on stuff.
When I visited my gran, usually once a week, I used to get 6d from her: Half of this, 3d, would go into the bank and the other half on a cone from the Italian café next door to gran's. When I was about seven my father began to give me pocket money too, but it was rather erratic, and asking for it was one sure way of ensuring it would not be forthcoming. Most weeks it was a shilling – that was 6d for the Saturday morning cinema, 3d for a comic to read and swap, and 3d for sweets. No thought of saving any of this entered my head. However, if I was given extra money then I would be allowed to spend some, but most had to be saved. So, for most of my life I’ve been a saver.