Welcome to the Helpful Gardener! Some great advice from Opabinia. Do use the largest cloves from the outer part of the garlic head as that will give you larger heads when you harvest. You might also find these sites helpful about growing veggies and veggies in containers.
One of the best things you can do to improve your clay soil is to add lots of organic matter. Compost is great for that. Since winter is on the way, you could do sheet (lasagna) composting over the winter and plant in spring.
I tried to use as many UK sites as I could.