Does anyone have any insight as to how much it matters whether or not I tick this box? I would prefer for references to be got after any interviews rather than before (once they know they want to hire me). Would it be a hindrance / potentially affect my chances if I don't tick this box?

Thanks!

Hi. My post is inference not based on knowledge. I do not think it will affect your chance if you tick that you do not want them to contact references before the interview. I think most of us would prefer that the references would not be contacted at all :) or at least before there is a high chance of getting a job offer.
I can fully understand where the problem is. Every referee has a "quota" for each applicant then she/he might get bored (I put she before he because of women's day, just kidding). You do not want to waste part of your available quota for nothing. I bet 90% of applicants would tick this box to "save" the response of the referee to important occasions.

TQ, I can only imagine they want to contact references before interview either as a upfront tool to allow them to select those suitable for face to face rather than wasting time interviewing someone whose references don't back them up, or, more likely, because once they've found a suitable candidate they don't want to mess about for weeks on end trying to get reference letters sorted out. Perhaps in their experience this latter stage has cost them good candidates before.
Either way, if they are asking for this, there's probably a good reason for it.

Unless you feel your referees could be inconvenienced by this I would probably advise not putting potential roadblocks in the way of any recruiter. Especially in a cut-throat game like academia where other suitable candidates are ticking that box.

I think if they contact your references before the interview you are more likely to get an interview. Talking with your references is probably a better way to sift CVs than just reading the CV. I don't think it will impact your odds of getting the job once you have an interview.

I know that for my postdoc after I accepted my offer to interview but not actually interviewed yet, they asked for my references. My supervisor was surprised that they did it that way as it isn't common. I know UCL ask if they can be asked before interview on their applications but then have a separate policy for research roles which states they ask after. Chances are they won't actually ask prior to interview.

Thanks all for taking time to reply. Most research jobs I've applied for have asked for references before or at time of interview, bar one where I was interviewed before references were checked. I decided not to tick the box this time and will see what happens. I figure if they really want to hire me then they will be happy to wait till after the interview to get the references. On the other hand, they might want to review references before inviting candidates interview. But in that case, they should say so and not give the option. Just to explain - I'm not too bothered about this job but thought I'd try applying and just see. I didn't want to bother my referees unless it comes to me being offered and wanting the job. If it was one I really really wanted I wouldn't risk not ticking the box.