The simple answer to your question is "Yes, you do require a licence". Playing recorded music 'in public' (which broadly means outside your own home) nearly always requires a PRS licence. (It's a requirement under the Copyright, Designs and Patents Acts 1988). The Performing Right Society is the only body which can licence businesses for the use of recorded music on their premises.
Licences for shops start from £75.90 per year (+VAT). That applies when only a single small portable radio is used. Otherwise prices start from £140.90 per year (+VAT) at the Standard Rate, which is what you pay if you get your licence BEFORE you use recorded music on your premises. However if PRS staff catch you without a licence, your first licence will be at the Higher Rate, which starts at £211.35 (+VAT). Major supermarkets pay well over £1000 per year.
Chris