Rigby and Peller isn't too far away (just off Old Bond Street) but it will depend how much you want to spend.

I went with my MOH and am so glad that I did (found out I've been wearing the wrong bra for the past XX years! and since I've changed it's amazing how much better I feel!) I think their bras start at £40.

If you have any dress material swatches or a picture of your dress they will recommend a style of bra to go underneath (e.g. not too patterned if very tight fitting, strap sizes etc.)

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Denver