Taking it literally, as I have below, you can use red, white and blue as a colour scheme for you wedding. Navy blue is a very popular colour at the moment and is great as a colour for bridesmaid dresses or your groomsmen's suits or ties. Red also makes a fabulous accent colour - why not use it for your wedding shoes if you'd like to make a statement or as a really striking bouquet.
If you want to be a bit more subtle with your theme you can simply use Best of British as inspiration. Maybe use only British suppliers or look for things which are quintessentially British - such as a red double decker bus for your wedding transport, have a street party theme for your reception or go for strawberries and sparkling English wine for your food and drink. I'm sure there's lots of different options - but here's some examples to get you thinking.
Gerbera bouquet - Taylored Images
Union Jack invitation - Dottie Creations
Red bouquet - Silesia Group
Place holder - Not on the high street
Bus - The Beautiful Image
Bunting - Not on the high street
Red shoes - One wed
Navy bridesmaid dress - Nordstrom
Cake - Cakes by Elizabeth Finch
There's even more inspiration on my Best of British pinterest board.