You can do work in people's houses, but you must certify your work to the current (Eighteenth) Edition of the Wiring Regulations. This is a legal requirement under part P of the Building Regulations in England. (Wales and Scotland have similar provisions.) The Wiring Regulations require either a Minor Works Certificate, or a Design Installation and Test Certificate for all wiring work.
If you carry out notifiable work such as installing new circuits, working in a kitchen, or installing a new consumer unit, in a dwelling then you must either notify the work to Building Control or be a member of a self-certification scheme such as NICEIC, NAPIT etc.
If you notify the work to Building Control they may require the certificates to be completed by a person with a current qualification. If you wish to apply to be a member of a self-certification scheme they will require you to have current qualifications or to be supervised by a qualified supervisor.
Small jobs which are non-notificable must still be certificated by you to the current Regulations and the certificate supplied to the customer. Forms of certificates are prescribed by the regulations and samples are available from IET.
The above applies to dwellings (including outbuildings and gardens). If you are working in non-domestic buildings then the notification requirement does not apply, but the Electricity at Work Regulations do (they would apply to you as a worker, and to your client as a business) and they would require a person to be competent. Evidence of competence is your qualification. For some work a 16th Edition qualification may remain satisfactory evidence of competence, for others it will not. For example, the Eighteenth Edition requires consideration of surge protection in designing an installation, and requirements for RCDs to all sockets and all concealed wiring even in permitted zones has changed since 16th Edition expired in 2004.