Estimate, a racehorse owned by the Queen and trained by Sir Michael Stoute, has tested positive for morphine, a prohibited substance, Buckingham Palace announced.
Initial indications are that the positive test resulted from the consumption of a contaminated feed product, the palace said.
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The operation to recover the unexploded bomb near the Houses of Parliament let to disruption in central London overnight.
Southern parts of England and Wales will see sunny skies after a frosty start.
A police spokesman said the incident in the Bourke Street Mall on Friday was not related to terrorism.