>>> But, from the .gov website:
"You don’t pay Stamp Duty, Income Tax or Capital Gains Tax on a property you inherit when you inherit it."
I don't think that's in dispute, NJ.
Mr Pinkcows definitely inherits the property free of SDLT. However if he needs to borrow money based upon a mortgage on the property (which would seem to be possibly relevant here, as there's clearly a mortgage lender involved in the situation somehow) and can't afford to take on that mortgage solely in his own right, he'll need to transfer half of the title to the property to Mrs Pinkcows, in order that they can get a joint mortgage. It's that transfer that is subject to SDLT.
This link, from the Government-funded Money Advice service would seem to support that view:
https://www.moneyadviceservice.org.uk/en/articles/stamp-duty-land-tax-transfer-ownership-land-property-england-northern-ireland
(See the somewhat analogous situation under 'The transfer is over the threshold' but note that the SDLT rate of 2% referred to there is for a sole home in the relavent price range. The rate in Pincows case is initially 0% - because the value of the property is less than £125k - but with 3% added on top because it's classed as a second home).