It is an interesting question. I hope you will tell us how UCAS respond, OP.
My guess would be that it would come down to one (or both) of two things.
Either a simple technical thing: the vast majority of job titles are not unique and are therfore not considered personal, identifying information, particularly as the question does not ask whose job title it is or any other information about that individual. There is an opt out option for cases where the person being asked considers that the information is identifying enough that it constitutes personal information.
Or, and much more interestingly, it may relate to how you resolve the issue of information 'belonging' to multiple people. In this case, your job title is information about your job, so it is your information and hence 'belongs' to you, but your job title also constitutes your DC's background, so it is also their information and also 'belongs' to them, particularly in this case where your DC's background is the subject and purpose of the question being asked. As it is not possible for your DC to disclose information about their background without also disclosing information about another, but not directly identified, person, and your DC can opt out of providing the information because it could potentially identify another person, it falls into something of a grey area.
As it could also be argued that the collection and processing of this data is necessary for the function of a regulatory body and is in the public interest, it would probably not be unreasonable for either or both of the above to be interpreted more leniently with regard to any possible consent requirements from people other than the individual responding to the question, particularly as they have the option of declining to answer.
Or it might just be that there is some small print somewhere that covers consent.