Helle
I was in the same situation as you 6 weeks ago here in NW London – deep cracks after 4 months of drought.
After about 7 inches of rain the past 6 weeks, the situation has completely rectified itself – I test the soil every two weeks with a fork to see if it will go to one full fork’s depth without trouble and all is well now coming to the end of September, whereas I was struggling to get to one half a fork’s depth six weeks ago.
Obviously, your transition into winter is sharper than ours here, so I wouldn’t want to advise, but if you get 4-6 inches of rain before the end of October and the temperatures aren’t too hot, I suspect that all will be well.
No doubt Charles can give more detailed advice……..