There are no licensing requirements relating specifically to shoe retailers.
However, if you plan to play background music in your shop you'll need to obtain a licence from PPL and from PRS for Music. There is an annual fee for these licences.
Any business which uses a CCTV system, or keeps records of individuals' personal details (for example for credit finance purposes) may need to register with the Information Commissioner's Office (ICO) unless they are covered by an exemption. You might keep records like this if you have an e-commerce or mail order business, for example. From May 2018 the General Data Protection Regulation has introduced additional protection for personal data. You can contact the ICO, Wycliffe House, Water Lane, Wilmslow, Cheshire SK9 5AF - or visit their website for more information.