Did it become easier to land an academic job in the UK after the Brexit referendum? This is a companion question to Why is Brexit bad for British science? Judging from the responses to that question, a significant number of academics are unhappy with Brexit and are not intending to stay in the country for the long term. The implication is that it's become easier to get a British academic position, since there are fewer people interested. Is this borne out in actual data? I'm particularly interested in whether the number of applicants for faculty positions / postdocs dropped, and if so by how much. 

The closest thing I've seen to this is Royal Society president Venkatraman Ramakrishnan saying they have anecdotal evidence of people not wanting to come / wanting to leave, but no statistical evidence. It seems to me it should be possible to get that statistical evidence, e.g. universities probably keep a record of applicants for each position, so if there's a change in number after 2016 it should be noticeable. There was no drop in international student applications, but it's not obvious if that also applies to faculty positions.
Fro the anecdotal evidence referred to by Venkatraman Ramakrishnan it appears that there are people who do not want to come to the UK post-Brexit. In your question you are implying a conjecture that the number of applications will fall and there will be easier to get an academic job in the UK.

The conjecture seems wrong to me. You seem to ignore the fact that the number of jobs in academia is not constant. Many jobs are funded by research councils in the UK but also EU councils like ERC. If this funding is going to reduce, so will the pool of available jobs. 

Teaching-focused academic staff are funded by the Universities directly and this funding depends on student recruitment numbers. There is a certain rise in the numbers currently following the cap lifting in 2014 but it won't last forever and can't compensate for the expected reduction in EU student numbers. 

Even if Universities disclose their records of application numbers for the academic posts (which is not likely), this information has to be compared also with the number of posts being advertised. Bear in mind also that with pound weakening, UK jobs are becoming less attractive for overseas applicants even on purely financial grounds.

To summarise, it is possible that the application numbers reduce and it becomes harder to secure an academic job post-Brexit.