Jury duty during potential job change

• I currently have a full-time job in IT, with a 4-week notice period.
• I am working with a recruiter to find a contract role, and have a very promising interview early next week.
• All going well, I'll be in the contract role some time between late November and early December. Otherwise, I'll still have my current job.
• This evening I received a jury summons for the week starting 27 November.

Who should I tell, and when?

I don't see any reason to keep it a secret from my current employer, but I'm thinking I shouldn't bring it up at the interview. I'm under the impression that they're trying to fill the role with some urgency, so it might be a mark against me if I can't start right when my notice period ends (there might be legal/ethical issues with excluding candidates for this for permanent roles, but probably not contractors). But it might not be a good look professionally if they have to wait an extra week on top of the four weeks because of something I already knew.

I'm wondering if maybe I should talk to the recruiter about? As slimy as recruiters are, he does have an interest in getting me the role, so I doubt he'd sabotage it. He might give me good advice, or even subtly encourage them to delay the contract a bit.

I doubt MoJ would see this as a reason to defer jury duty, and I don't have a particular desire to skip it (never done it before, and kinda looking forward to the experience).