Do you have to do a snag etc or are you ready to go?
Your solicitor will have to investigate the title deeds once s/he receives them from the vendors solicitor. If the title deeds are in order, your solicitor will complete the lenders documentation in the offer pack they received and return them to the lender. They will also comply with any additional conditions of the offer that the lender may have asked them to do. Check in with your solicitor to see if everything is in order. If they have any concerns, they will let you know and can give you an expected timeframe.
In the meantime you can ensure any offer conditions are complied with e.g. your life assurance and fire cover are in place etc.