Mortgage: changing jobs before exchange of contracts?

Me and my husband started a mortgage process in June and we are currently in the stage of "searches". We also do not know a completion date as the property that we selected is tenanted.

At the same time, my husband got a new job, and I also gave in my notice in August so we are both employed by our current employers until the end of October.
(I am also in job hunting so hopefully I will find a new job before)

I am worried that we will lose the mortgage if the completion will not happen by the end of October. And not sure what checks the bank might have on us before granting the mortgage to us… Can anybody give some advice or went through same?

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