Crawford stars as villain Count Fosco in the production, which held a benefit premiere Monday at the West End's Palace Theater for the Prince's Trust Charity, BBC reported Tuesday.
Prince Charles and Camilla Parker-Bowles met the stars and Webber backstage.
Crawford, who last starred in the West End in 1986 in "Phantom of the Opera," admitted he was nervous.
"It's always nerve-racking," Crawford said to Charles about his return to the stage.
Crawford's last Broadway production, "Dance of the Vampires," closed after seven weeks and lost $13 million.