Here's a few things I'd do (I've only considered end-state, not transition to that)
VAT Threshold
At present, a small business (under £90k turnover) doesn't have to register for VAT, but if they have higher turnover they have to charge VAT on all the goods/services they sell, not just those in excess of the threshold. This massive change when they cross the £90k line is a big disincentive to them growing.
So instead only charge VAT on turnover in excess of the threshold.
Fund this by decreasing the level at which the threshold is set
National Insurance
At present, earned income is taxed at a higher rate (Income Tax + NI) than unearned income (Income Tax, but no NI).
Level the playing field by reducing employees' NI contributions to £0, and increasing Income tax, so that overall it is revenue-neutral
Marginal tax rates
Make it so there is never a scenario that the marginal rate of tax is higher for a lower level of earnings than it would be for a higher level of earnings.
Stopping "accidental" fiscal drag
Change the way that governments state tax thresholds and bands. So instead of saying "the personal allowance is £x", they'd say "the personal allowance is x% of median earnings", and instead of saying "the higher rate threshold is £x", they'd say "the higher rate threshold is the xth percentile of earnings". That way we don't have stealth tax rises, with more people paying tax due to inflation. Governments can still change the thresholds but have to be explicit about it.
Local taxation
I used to think that replacing council tax with local income tax would be a good idea, but I now don't, partly because tax on income is more easily avoided.
I would keep a tax based on property values, but not base it on what a valuation which is ~30 years out of date, and not have only a limited number of bands. Instead I'd charge a flat percentage of the taxable value of a property, and "the taxable value" would be the current market value minus an allowance which is the value of the 5th percentile of house value in the country..