While surfing on another topic I came across a reference to A. France & Sons, Funeral Directors, who arranged the coffin for Lord Nelson's funeral and are still trading:
https://www.afrance.co.uk/history-of-the-firmThere are a number of firms who supplied Nelson that are still in business, often in the same premises in, or around Jermyn Street. Locke's the hatters, who made his hat with the eyeshade, are still there, as are Floris, from whom he bought White Rose scent for Lady Hamilton before he left for Trafalgar; his tailor's, Gieves and Hawkes, still make military uniforms; Dolland's, who supplied his telescopes, are now part of Dolland and Aitcheson, the opticians.