Of course, status is multidimensional, so to say it's "zero" is a bit immoderate. I studied CS in the UK (Cambridge) and I'd agree that it's not a prestigious field. Having said that, CS academics are generally fairly well off, some being posher than others. I think a major factor in the low status is their lack of cultural knowledge (cultural capital), even if they know or are related to others who do have it.
Much of what can be said about CS in the UK is true of the "technical middle class" in general.
https://en.wikipedia.org/wiki/Great_British_Class_Survey#Tec...
"The technical middle class, about 6 percent of British society, shows high economic capital, very high status of social contacts, but relatively few contacts reported, and moderate cultural capital. Occupations represented include medical radiographers, aircraft pilots, pharmacists, natural and social science professionals and physical scientists, senior professionals in education establishments, and business, research, and administrative positions.[17]
The technical middle class is relatively well to do, with an average household incomes of £38,000, average savings of £66,000 and houses worth an average of £163,000. Members of the class report the lowest number of social contacts of any of the classes, though these do tend to be high status, probably mostly other professional experts. It is relatively culturally disengaged with both highbrow and emerging culture. Women comprise about 59 percent of this class. Many of technical middle class do research or scientific and technical work; a portion of the graduates are from established and prestigious universities with strong reputations for science, such as University of Birmingham, University of Warwick, University of Cambridge, University College London, University of Southampton, and Imperial College London with degrees in science and technology. Many of the technical middle class live in South East England where scientific and technical jobs are to be found. If they live in an urban area they live in the suburbs. Many of them have middle-class origins but are less engaged socially and culturally with the arts and humanities."