Brown, 50, wore a dramatic white gown by Evelie Bridal Boutiques, while McPhee, 37, wore a red tartan kilt.
Fellow Spice Girl Emma Bunton attended with her husband Jade Jones and son Beau, alongside other celebrities including Daisy Lowe, Katherine Ryan, and Angellica Bell.
Preparations for the event included decorating the cathedral's front with white and yellow flowers and a bagpiper playing for guests' arrivals.
Victoria Beckham was unable to attend due to prior commitments abroad but sent a congratulatory message to the couple on social media.