Do I start work before my induction or not?!

So I am due to start a new job next week, in the UK.

When I told them my earliest start date based on leaving my current role, it was Monday 29th. Since then I have completed the onboarding process on their online portal (medical questionnaire, references etc) and then received an automated email to say my induction would be Monday 29th at 9am.

Fine, no issue.

Then the HR lady rang me to say that the induction has moved to the Tuesday 30th (something to do with an external provider changing days) so my induction would be 30th but they'd honor employment from 29th.

Also fine. I followed up on email to make sure my anxiety riddled brain hadn't dreamt it the following day.

I'm now panicking (new job anxiety is high right now!) if the assumption is I should turn up on the Monday or not. Every place I've worked, you don't start before induction. It's food manufacturing so there is some fairly important regulations they have to take you through before you can go in the factory. And I've managed people who I also wouldn't allow to start before induction because they wouldn't have their key fob or pass yet. But every business is different.

I'll also add that when I went into the new job to meet the team, I did state I'd start on the Tuesday but only to my colleagues, not the manager as he wasn't in that day.

I'm too embarrassed to send another email so late after the previous to clarify and dont want to be labelled as the stupid person before I even start.

What should I do?