Yes, trickledown works.
Intuitively trickle down is a great idea. You give your highest income groups some more money, they decide to have a swimming pool built, the swimming pool companies can'y keep up with demand so take on new staff, unemployment falls, aggregate demand in the economy rises. However, it's only intuitive.
I'll try to keep this simple:
Economics uses a concept called marginal propensity to consume (MPC) - the proportion of any extra income is spent. Trickle down's effectiveness depends upon MPC being high in high income groups, it also depends upon MPC being constant over time.
Empirical evidence suggests that the richest groups in society actually have the lowest MPCs. MPC falls as you get richer. MPC is higher in middle and lower income groups. So, if the government's objective is to generate economic growth a more effective policy might be to cut taxes for middle and low earners. The 'young' have the highest MPC as changes in their consumption habits tend to track changes in income.
Remember as well that attitudes to spending will change over time so while cutting taxes for the rich might have been effective in 2004 it probably won't be in 2012 due to low levels of confidence. Don't make the mistake of thinking this is constant.
This is why the NMW has been so effective in raising consumption and aggregate demand it's BECAUSE it raises the income level of low earners. They go out and spend 100% of their net income (not necessarily a desirable outcome by the way) and that generates jobs.
As I said, I tried very hard to keep this as simple as possible. This is what I believe.
I have't found accessible MPC data by decile for the UK so I'm troubled that I can't back these statements up.