Prince William said Tedworth House made him and his brother, Prince Harry, "very, very proud" as he declared the recovery centre officially open.
He said: "It is an enormous pleasure to be here at Tedworth House. This place, and what Help for Heroes and its partners have done here, makes Harry and me very, very proud."
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Outbreaks of rain and strengthening winds will affect southernmost parts of England and Wales today.
An earlier debate on the issue was suspended as an 'expression of support' following the Westminster terror attack.
Five people were killed and dozens more were injured after a car and knife attack in the capital on Wednesday afternoon.