Requirements for open job advertisement by universities in the UK?

Perhaps I should clarify. What laws constrain employers from simply hiring an internal candidate without advertising a position, or from having a sham advertisement in order to hire their internal candidate?

No laws prevent a uk company or institution from hiring an internal candidate, so there would be no real need to run a sham job search to do so. In fact there are specific laws protecting staff on fixed term contracts which give them the right to ask to be considered for suitable vacancies opening as their contracts end: so for a lectureship, if a suitable post-doc existed they could simply be offered the post. The major risk of not running a search is being sued by a potential candidate under equality/discrimination law, if they can make a case they they have been unfairly disadvantaged by not being given the opportunity to apply. The only time an advert is compulsory is if you are trying to hire from outside the EU, in which case you have to run a full search to prove that you could not recruit someone with the same skill set from within the EU. There are laws then relating to this hire and its conditions, which stem from Immigration, rather than employment law. In terms of your original question about the advert and its time period: from a recent experience in uk higher ed we had to let it run for at least 4 weeks to comply with immigration in case we got a foreign candidate, and be very careful with our wording under the equality act. In terms of short listing there are also some rules about positive discrimination for people with disabilities, but it doesn't sound like that's relevant to the question? If a Uni has gone to the effort and expense of running a search, with adverts and interviews, I would assume they genuinely thought someone could be better than their internal candidate, or they hoped external advertising would broaden their diversity.

Under what laws could they be sued by a potential candidate under equality/discrimination law, and does that only apply to protected characteristics?

Yes, it only applies to protected characteristics, and the most recent legislation is the http://www.legislation.gov.uk/ukpga/2010/15/contents. (Of course, if the applicant is a foreign national, this is modified by our immigration law, which means that an equally qualified UK or EU applicant must have preference over an overseas candidate, regardless of equality issues). There's some basic info from ACAS http://www.acas.org.uk/index.aspx?articleid=4657 (bear in mind that ACAS consider it 'best practice' to consider retraining an existing employee first before conducting an external search).