scientists at Birkbeck, University of London and UCL?

English universities are subdivided into colleges. Birkbeck is one of the colleges of the University of London, and specializes in night classes for those who wish to complete or expand their education, although it offers many other educational opportunities as well. Birkbeck also has campuses elsewhere in England, other than in London. UCL means University College London, and was the first "separate" college of the University of London. It was opened in 1826 to provide educational opportunities for people from any religious or social background, and it was the first institution of higher education in England to offer the same course work for women as that offered to men. Prior to the opening of UCL, university colleges in England educated men only, and usually only men who were the members of the upper classes. This was not because they discriminated by social class, but because they accepted students from what the English call public schools (which in the United States would be called private schools), and only the upper social classes, and the wealthy could afford to send their son to public schools.

Universities in England were first established to train young men to become members of the clergy--ministers of the church. When Henry VIII created a Protestant reformation in England, that meant that these young men were being trained to be ministers in the Church of England. Certainly many young men educated in those universities did not become members of the C of E clergy, but in practical terms, they did not educate people who were not members of the C of E, they did not educate women and they did not educate other people in the British Empire, but only young Englishmen. UCL broke that mold.

That is informative.

The question is:

Does "scientists at Birkbeck, University of London and UCL" refer to "scientists both at Birkbeck subdivision of University of London and at Birkbeck subdivision of UCL"?

Actually, that is not what your original question asked. However, both Birkbeck and UCL are subdivisions of the University of London. Birkbeck is not a subdivision of University College London (UCL). Therefore, to restate this in terms of your modified question: ". . . scientists at Birkbeck College, University of London, and at University College, University of London.