Tbh, I don't really care if people view sex work as not being work. What does concerns me is once sex work is considered to be actual 'work', then the DWP can push sex work as a viable option and sanction those who refuse to pursue this path - I think sex work should only be undertaken by those who choose to do it, not those who have been pushed into it.
The DWP is just plain evil at the moment but then we have a screamingly evil government in power. DWP plans to push people into any job at any price have met with huge pushback from business and rights activists. The DWP are also refusing to release their own reports which are reported to confirm these policy paths are disastrous and harmful and make no economic sense.
As for government refusing to acknowledge sex work as work I don't know if this is for reasons of dogma or because of legal issues with consent and contract law and taxation. It may be worth approaching the Law Commission for a view.
The government website has a report. (Search for " Nature of prostitution and sex work in England and Wales. Research report produced by the University of Bristol on the current nature and commonness of prostitution and sex work in England and Wales.") The preamble gives a good breakdown of the type and variety of sex work, who practices sex work, and while the language is soft very usefully highlights how poor public policy and discrimination may form an environment where the state effectively pushes or coerces people into sex work. They also note that the Home Affairs Select Committee published a report on prostitution which was leaning towards a more progressive view.
I personally feel that porn needs better regulation. I am not happy that mostly large America tech companies dominate the porn industry and turn the almost always exclusively male owners into multi-millionaires or billionaires. Nor am I happy with tasteless porn which encourages bad habits. The Guardian in the column "When it comes to porn’s damaging effects, millennials and Gen Z feminists are united" is hyperventilating and appropriating feminism to shut down sex positive feminists. I feel they are going to far and not helping progress public policy development to balance women's agency and safety with consent.
I know it's a political comment but I do not see this government doing anything about poverty nor making sex workers or women's lives easier.