The advert for an "honorary research assistant" in graduate painting appeared on the website of the Slade School of Fine Art, part of University College London, until the closure of applications on Monday.
The appointee to the unpaid role is expected to commit themselves to working one day a week during term time for a whole academic year, starting in the coming spring term.
They will be expected to "provide research assistance for special research projects", and be "an active and visible presence in the graduate painting area and contribute to the research culture in the school".
In return, the appointee will have access to UCL resources, such as its library, and "may have negotiated access to technical facilities at the school to carry out their own research and artwork". They can also make research grant applications "in conjunction" with the school.
The advert follows the withdrawal either this year of an honorary research post advertised by the University of Birmingham's School of Psychology and an unpaid internship offered by the Anna Freud Centre at UCL.
In a letter to the UCU following the latter withdrawal, UCL explained that the centre was an independent charity that was "not party to UCL policies". It said that although UCL offered unpaid short-term work experience positions, "we are very clear that these opportunities are not to replace paid work positions or to cover regular or recurring work in a department".
UCU general secretary Sally Hunt said the latest advert "flouted" that policy.
"Both previous efforts, by UCL and Birmingham, to acquire researchers for free were removed because of an outcry from the academy. Failing to pay researchers undermines the principles of equal pay, is clearly discriminatory and will not be tolerated," she added.
"I am amazed UCL thinks this is acceptable or unlikely to damage its reputation. Universities should be striving for excellence, not seeking to exploit those who might be able to afford to work for nothing as free labour."
A spokeswoman for UCL said that, unlike the Anna Freud Centre position, the Slade advert was for "an honorary position for somebody already working as an artist".
"The position is not about training, work experience or to 'cover regular or recurring' work," she said. "The school is overwhelmed by artists wanting to come and work with them, so they wanted to streamline the process in order to improve equal opportunities."