If the phone is carrier blacklisted in the U.K. it won't work there. If the UAE does not share the U.K. Blacklisting database (which it most likely does not) then it would work there, or anywhere else that doesn't use the U.K. Blacklist.
Carrier blackilisting is not universal. If a device is stolen in one country, and reported and blacklisted there, it will often end up being sold in another country to avoid the blacklist.
For example, in the USA all carriers share a blacklist, and that in turn is shared with carriers in Canada and Mexico. But outside of those three countries, the USA universal blacklist won't have any affect elsewhere.