The term "Hall of Science" was first used by the Owenites for their meetings places, which were also used for educational purposes. Some of them appear to have been specially built, but others were no doubt in existing buildings. In later years, after the Education Act of 1870, those that were still active were incorporated into official Departments of Education. This whole subject deserves more research. I give the leads below that I have found, mostly on the internet.
In the journal "The Vocational Aspect of Education" (vol 12, issue 25, 1960, published by Taylor and Francis Group)
there an article, based on an MA thesis on "The Sheffield Hall of Science", by John Salt.
"The Sheffield Hall of Science, opened by Robert Owen on March 17, 1839" ...
"Agreement to teach the classes of the Pestalozzian School was a condition of G. J. Holyoake's
appointment as lecturer at the Sheffield Hall of Science by the Socialist Congress which met
in Manchester in 1841." ... "The Sheffield Hall of Science may have functioned effectively
for a decade only, but educationally Owenism left a lasting legacy."
Edward Carpenter spoke there, or at its successor: "Co-operative Production: with reference to the experiment
of Leclaire. A lecture given at the Hall of Science, Sheffield, 1883. Published by John Heywood, Manchester, 1883.
Edward Carpenter Archive bibliography
"During his first visit [to Manchester], Engels attended the Hall of Science, which was
only five minutes from Ermine and Engels office. At weekends upwards of 3,000 people would
attend lectures here on English social and political matters. It was a hot bed of radical
activity. Chartists and socialists would meet there, to exchange ideas and circulate
literature. Here he met Owenite socialists, the secularist John Watts, as well as leading
Chartists such as James Leach and Julian Harney."
BBC Legacies Local History
"Hudderfield may boast the last of the Owenite Halls of Science. Now tucked away in a back street, this building,
then surrounded by fields outside the town, was for a few years from 1839 to 1844 the centre of Socialist and other
Alan Brooke Local Huddersfield History
One of Edward Avelings works is: "The Plays of Shakspere ... The Substance of Four Lectures
Delivered at the Hall of Science, London". Freethought Publishing Co., n.d. .
This exchange of questions and answers published in Hansard mentions
Edward Aveling, Annie Besant, and Alice and Hypatia Bradlaugh in connection with
the Education Department - The Hall of Science, Old Street (1882).
Charles Bradlaugh also spoke there: "And there are some interesting leads in a series of lectures on
Anthropology given by CB in 1881 at the Hall of Science. These are interesting for several reasons.
First, they show CB in the role of scientific lecturer. Significant, because he isnít just debating
churchmen or attacking the Bible" [This text no longer appears at the link alas.]