That's a Pegler (Bulldog is a rebadged version) valve. The flat topped/domed actuator does move up and down - but not by a lot. Just a mm or two.
The (carp) heads have a relatively soft black plastic 'pin' that appears to have broken off / is missing in the centre of the white clips that fix to the valve... They can also distort making them ineffective in moving the valve actuator. https://files.ekmcdn.com/plumbersma...-head-07000730-(2)-1834-p.jpg?v=262021-135904 shows the pin in the TRV (just).
The centre chrome pin will not move at all. There is a black pin at the top in the centre of the white clips in second pic which moves up and down but doesn't show in pic as is too dark. Wasn't sure whether the chrome pin in centre of nut was the one that should move up and down. Our other rads have a much thinner one like a pencil lead which is shown on the youtube vids. Never seen one as thick as this one and wondered if hitting it to try and release it would do more harm than good.
Put a drop of oil on it ,leave it for an hour,then try pressing down heavily on it, putting a block of wood( or similar) on top would enable you to apply more pressure.
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