Should the United Kingdom Government rely on market forces to redistribute income and wealth, to make it fairer or intervene to do so?

Market forces can lead to a fairer distribution of income from the trickle down effect. This is where those on high incomes will spend their money, which creates demand for goods and services, as a result the demand for labour increases ( this is because the demand for labour is derived from the demand for goods and services). Due to the increased need for labour, individuals take up employment; thus acquire new income with which they can buy assets and increase their own wealth as the distribution of income and wealth is mutually reinforcing. This shows how free market forces can lead to a more equal distribution of income. However, the extent to which this may happen may depend on the rich's marginal propensity to save (how much of their income they save) if this propensity is very high, then the demand for goods and services is unlikely to rise much, as a result the demand for labour isn't going to rise and the newly found income will be minimal, meaning the distribution of income is unlikely to become any fairer. The opposite is true if the MPS is low, therefore making the idea to leave the distribution of income and wealth to market forces hold weight.
On the other hand, the Government could intervene to make the distribution of income fairer by taxing income more progressively and then distributing via transfer payments to those who need it thus making the distribution of income fairer. But this may have unintended consequences for the government, as Arthur Laffer would argue that increasing the tax take beyond the efficient level will yield a lower tax take, due to migration, tax evasion and tax avoidance. This then leads to the unintended consequence of a loss of entrepreneurial spirit within the UK which would mean that business ventures by individuals will be few in number leading to fewer job opportunities thus a reduction in the extent to which unemployment decreases. But also as individuals want to avoid this higher tax rate and take part in capital flight, we may see less investment in the UK and therefore see productivity slump thus international competitiveness may lack as a result having negative effects on the UK's balance of payments on the current account. This means that higher progressive taxes can have large unintended consequences and then lead to government failure.