During the Sew Along many questions that pop in my mailbox where regarding where do I gather my supplies, specially relating to tailoring and specialist tools. There are many excellent suppliers available in London (some have online stores) and the following are the ones I recurrent use. None of my following recommendations are sponsored. You will notice that some stock an exhaustive selection of sewing supplies, while others only a few.
Professional button makers: DM Buttons
Ps: If you love looking at antique sewing tools, have you seen this?