Legal ownership of UK shares used to be determined by share certificates, but is now captured electronically on the register of share ownership for each firm, which is updated after every share transaction.
Usually a broker records shares bought on behalf of clients using a general ‘nominee’ account on the register with a name chosen by the broker. Nominee accounts are preferred because recording many shareholdings under a single name reduces administration time and cost, since share certificates are not issued.
However, some investors prefer to pay extra for share certificates and to have their own name on the register. This can make identifying their shares easier and quicker should a broker go bust.