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www.parliament.uk for example but on the whole most of these have been cleaned up.
Therefore you can only register
.co.uk, .org.uk (& .net.uk)
there are others .ltd.uk .plc.uk, .sch.uk .ac.uk etc. but these are for restricted groups.
Before Nominet a very few select groups got one:
Parliament, MOD, British Library, National Library of Scotland and the worlds most powerful nuclear fusion reactor based in Oxford.
I only know of one private company that got one: A web designer in Newcastle who had the cheek to call himself The W3 Organisation and registered org . UK
Today it is a one page site his wife has just sold.
ac.uk Higher and further education and research institutions
gov.uk National, regional, and local government bodies and agencies
mod.uk Military and related purposes
nhs.uk National Health Service
police.uk Police forces
.nic.uk Network use only
do exist, but arn't looked after by Nominet, plus oddities like parliament.uk