In the UK, “Institute” is a protected term, for which you need approval from the Secretary of State to use in a business name, per https://web.archive.org/web/20080913085135/http://www.companieshouse.gov.uk/about/gbhtml/gbf3.shtml. I’m not sure how this changes if you’re being a part of the university, but otherwise this could present some problems.
In the UK, “Institute” is a protected term, for which you need approval from the Secretary of State to use in a business name, per https://web.archive.org/web/20080913085135/http://www.companieshouse.gov.uk/about/gbhtml/gbf3.shtml. I’m not sure how this changes if you’re being a part of the university, but otherwise this could present some problems.