Princess Tributes
Flags across the district were flown at half-mast and a book of condolence has been opened at the Civic Centre in Ham Road, Shoreham.
The first person to sign the book was Adur council's vice-chairman Maurice Pitchford (pictured).
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Hide AdMr Pitchford said: "I have to regret that council chairman Don Phillips is not here, but I am sure he would join me in sympathy with the Royal Family. Hers was a life of some happiness and a lot of unhappiness."
Lancing MP Tim Loughton said: "One feels particularly for the Queen Mother and the Queen at this time and it is a sad start to jubilee year.
"Yet Princess Margaret was a great public servant and made tremendous sacrifices in her personal life, and for that, she should be remembered with great affection."
The Princess's funeral is in Windsor tomorrow (Friday) afternoon.