The simple answer is no they don't but they should take "reasonable" steps to find out that the employer is managing any risks. In a low-risk scenario like a normal office environment this could be achieved by a phone conversation discussing the placement's role, any associated risks and precautions.
The issue of work placement H&S was highlighted in a recent dispute when a Devon secondary asked parents to pay £33 to cover 'regulatory health and safety checks' for work experience placements. They were actually passing on a charge for a third party to carry out H&S checks on behalf of the school. In some cases schools will be unsure of how to interpret guidance from the HSE and will err on the side of caution in safeguarding their students and reputation by bringing in an expert. However in a statement sent to local news website DevonLive.com the HSE clarified the regulatory position for schools:
The claims made in this story by the school in question are incorrect and conflate the school's own policies with any legal obligations set out by UK health and safety law (of which there are none). There are no health and safety regulations that require schools, colleges, or those organising placements on their behalf, to carry out assessments for work experience placements. There is also no requirement for any prescribed level of occupational competence or qualification for education personnel, or others organising these placements.
It is not for schools, colleges, or those organising work experience placements on their behalf, to assess workplaces. The employer who is taking on the student for work experience has the primary responsibility for their health and safety. However, schools, colleges and placement organisers do need to take reasonable steps to satisfy themselves that an employer is managing any significant risks. For many low risk premises a visit will not be necessary; there is no reason why this couldn't be done over the phone with placement organisers simply making a note of the discussion. A conversation with an employer could include finding out what the student will be doing, what the risks are, and how they are managed.
It is about keeping checks in proportion to the environment, and in many cases it is likely that a school, college, or other placement organiser will be familiar with employers they use regularly and will be aware of their track record. They may also know of other schools, colleges, and placement organisers who have placed students with the same employers and can share information with them.
Finally, a separate risk assessment is not required specifically for work experience students, as long as an employer's existing assessment already considers the specific factors for young people. Furthermore, there is no requirement to re-assess the risks each time an employer takes on a new work experience student, provided the new student has no particular needs.