[UK] HireRight - job offer is contingent upon passing background check. Would it be stupid to hand in my notice?

I am due to start a new job at the end of august. I have received the contract and signed it and I noticed there is a section on the background check, stating that the offer is contingent upon a clean and clear background check. I was then sent the background check to complete with HireRight.

Everything on my CV is accurate and I have no criminal record. My work place is super toxic and I just want to hand in my 4 weeks notice but I feel as though that may be a mistake and I should wait until everything is 100% set in stone.

For anyone who’s had this check done, how long did it take for you?

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