Interesting question. Its plausible that there are not many vessels that are UK flagged anymore.

The more interesting question is how many of these are under "control"/influence of domestic operators

If required, a flag can be exchanged in a pinch and tax codes /regulations can be adapted to allow/encourage this.

Happened during the Falklands War.

There are peacetime rules and war time rules, war time rules are best summarised as “government does what it wants and justifies it after the fact”.

https://en.wikipedia.org/wiki/Falklands_War_order_of_battle:... under “Ships taken from trade”.

I just clicked through to some of the listed ships and it appears they were all flying a British flag in 1982 before being requisitioned.

It’s not at all clear to me a government would have that power about a foreign flagged vessel, even if the shipping line owning it might be British.

Maybe not legally, but most of the countries used as a flag of convenience are tiny, what could the Marshall islands do about it?

It's about a thousand ships, but realsitically it's very fuzzy, with flags of convenaince and all. And British companies own a _lot_ of ships, just flagged under other countries.