When you paid over your booking deposit, the auctioneer should have asked you for your solicitor's details. The vendor's solicitor will send the contracts to your solicitor. Your solicitor will check the contracts, title of the property etc. Your solicitor may have queries to put to the vendor's solicitor. If and when your solicitor is satisfied that everything is in order, you'll make an appointment to go and sign contracts. At that point you'll agree a closing date. The closing date can be shortly after signing contracts if all parties are agreeable and you seem to have most of your ducks lined up already.
If you've only just paid the booking deposit, it's unlikely that you'll be closing in early November. The various stages of the above process typically take weeks or months to complete. If you want a quick close, then both your solicitor and the vendor's solicitor will need to be willing and able to move very rapidly for you, as well as your lender.
As said above, you should speak to your solicitor who will be able to talk you through this process in more detail.