Word or phrase to refer to self-employed professionals working from home in the UK?

The term homeworker is only vague in the context you wish to use it in because it means someone who works from home. That person may or may not be self-employed.

The term freelancer is inappropriate in your context because whilst normally they would be self-employed it refers to someone who is hired for work on an ad hoc basis and they may or may not work from home.

The only phrase that meets both your requirements of self-employed and someone who works from home is self-employed homeworker.

There is an acronym, SOHO that refers to small office/home office but is generally used to differentiate market segments rather than refer to individual people. You could within the right context use self-employed SOHO worker or workers.