The case for taxing wealth, argument by argument.
Far from being unproven, UK wealth inequality is documented and rising: the IFS Deaton Review finds the middle-to-top wealth gap grew from £299k to £432k in real terms after 2006, and the ONS finds the wealthiest 10% of households hold 41% of all wealth. Housing and pensions are 75% of household wealth and both are concentrated at the top.
The UK's most comprehensive recent study of inequality documents a widening wealth divide: the gap between middle and top households (5th vs 9th wealth decile) grew from £299k to £432k in the decade after 2006 — from around 10 to about 16 years of average earnings. Home ownership for people in their 20s and early 30s fell from 55% to 35% (mid-1990s to 2017) as real house prices rose 170%, and 14% of people in their 60s now own two or more properties. Pension wealth is the fastest-growing component of wealth, and while ethnic income gaps narrowed over 25 years the ethnic wealth gaps stayed vast, with regional divergence largely housing-driven. Wealth inequality in the UK is not unproven — it is measured and growing.
Wealth is far more concentrated than income: the wealthiest 10% of households held 41% of all wealth and the wealthiest half held 91%. The "top 1% pay X% of income tax" claim ranks people by taxable income, not by wealth — and much of the largest fortunes (capital gains, assets, unrealised gains) is taxed lightly or not at all, so income-tax shares are not a measure of what the genuinely richest contribute.
The Bank of England's quantitative easing programme expanded by an estimated £300–£450 billion over the pandemic, taking total asset purchases to £895 billion. By design QE inflates asset prices, and the Bank's own analysis and the Lords Economic Affairs Committee noted it disproportionately benefits existing asset holders — i.e. the wealthy — widening the wealth gap, while the distributional effects were never properly measured.