You would say that Welby is an ex officio member (or a member ex officio) of those two bodies.
In this case, the Latin noun officium means 'A regular (esp. official) employment, charge or position, post, office' (definition 6 in the Oxford Latin Dictionary) – or perhaps 'What one has to do to fulfil one's role, a person's function or job' (def. 4). The preposition ex is expressing cause, I suppose: 'As a result of, in consequence of'
The New Oxford American Dictionary defines the term as 'by virtue of one's position or status.'
Eugene Ehrlich, Amo, amas, amat and more: how to use Latin to your own advantage and to the astonishment of others (Harper & Row, 1985) has this summary:
Officers of an institution usually serve on many of its committees not because they have personal qualifications needed on the committees, but because they hold certain offices. Thus, the chief executive officer of a corporation usually is a member ex officio of all the important committees of the corporation.