MymsMan is a UK resident but not a US citizen who has US sources of income. The terms of the UK US double tax treaty therefore apply to his US sources of income.
The UK has recently changed the taxation of dividends from UK companies, with the abolition of the notional 10% tax credit and the introduction of a dividend allowance. Most dividends from non UK companies and most distributions from non UK mutual funds are taxed in the same way as UK dividends. As an exception, distributions from mutual funds that invest in bonds is taxed in a similar manner to interest.
The US generally imposes a withholding tax of 30% on dividends and mutual fund distributions. As a UK resident MymsMan may apply under the double tax treaty to reduce this to 15%. The 15% withholding tax may then be claimed in his self-assessment against UK tax on these dividends and distributions. (If the claim is not made under the double tax treaty the UK would only allow a credit for the 15%.)
MymsMan should also note that on a sale of his US mutual funds, any gain (which is computed in sterling terms, using the exchange rates at the time of the purchase and sale) could be charged to income tax (rather than capital gains tax) under the Offshore Income Gains rules. The OIG rules would apply unless the mutual fund was a reporting fund (to HMRC not the IRS) and few US mutual funds choose to be reporting funds. There is a list of reporting funds on the HMRC website.
I shall leave it to others to comment on pension income.