Democratic Unionist Party councillor Ruth Patterson described the vote to remove the Union flag as "divisive, destructive and disrespectful of anything remotely Protestant, anything remotely British".
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After a showery start to the day, parts of Northern Ireland, western Scotland and south-west England will see drier conditions.
England have beaten Australia 44-40 in the third Test in Sydney to seal a 3-0 series victory.
France's foreign minister called for the UK to trigger the exit clause after a meeting with counterparts of the six EU founding states.