Interesting to note that Civvy firms are now asking for a 3 month notice period depending on what you are doing of course.
The last 2 permy jobs I have done in IT (Business Intelligence) have asked for 3 months notice.
I have lost a few interviews and at least one job because I cannot get out any faster. Used to be a month notice - long gone in my game.
In the end I just had to say I could get out in 4-8 weeks and hope for the best. Luckily I have managed to get out in 8 weeks.
Good luck.