CEF are wrong.
But 240v LED usually use GU10 bases, whereas 12v lamps usually use GU5.3 bases. So you would need new units with GU10 bases.
So the link to the LEDs in screwfix will do the job?
Are you sure that they weren't simply saying that lights identical to the ones the OP has are no longer available, so that if he wants them to all look the same, he'll have to replace all four, including the one which is still working?
Kind Regards, John
And no they actually said "you need to rip the whole circuit out and install new ones" nothing to do with the visual aspect of them!