Interest rates are payments made when repaying a loan, and are also the reward for saving. Lowering them, should, disincentivise saving and encourage spending. Lower interest rates will increase consumers' disposable income, leading to a rise in consumption, which raises aggregate demand and leads to growth in GDP (this can be shown by an outward shift of the aggregate demand curve). Demand-side growth such as this could create demand-pull inflationary pressures, which may impact the countries balance of payments current account in the long run.
However, this may not always be the case. We assume that a larger disposable income means higher consumption, this depends on the consumer's marginal propensity to consume and import. In an economy, such as the UK, a consumer is likely to increase their imports, indicated by the UK's large trade deficit. Consumer confidence is another important determinant of spending that must be considered. Furthermore, we could argue that, for some countries, falling interest rates may not affect disposable income significantly given that renting property (not taking out a mortgage) is more common than buying. However, this is more applicable in continental Europe. We could also argue that interest rates are more likely to affect investment rather than everyday spending. This would have greater supply-side effects, which implies more long-run growth. Moreover, this is likely to mitigate inflationary pressures, as can be shown by an outward shift of the aggregate supply curve. There are also other implications of lower interest rates, such as withdrawal of short-term financial flows, or 'Hot Money' from the UK.