Is it reasonable to ask for 2 months before my start date at new job?

I got a new job months ago, but this job requires advanced security clearance that takes months to process which is why i have not started yet. Good news is that I had notification back today that its passed, i will be having a call with them Monday to agree a start date.

I have just recently moved house that im now renovating and to be honest i was expecting the security clearance to take longer so i handed in my notice early at my current job already so i could have time off in between jobs to renovate the house, but also give myself a break between jobs to refresh.

i finish my current job 15th august, I'm on holiday 20th - 30th august so i wouldn't start then anyway.

Is it reasonable to ask them for a 2nd October start date?

i think this is ok but i wanted to get opinions.

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