If time permits, make this a day or two in advance; it gets even better as the flavors meld.
Beat together mayonnaise, cream cheese, garlic, Worcestershire sauce, horseradish, paprika, and cayenne with a mixer on medium speed until smooth, about 2 minutes.
Stir in cheeses until well combined. Refrigerate until cold, at least 1 hour and up to 3 days.