Hi Alison - whilst it can vary invariably such applications will trigger the need to serve notices on third parties as appropriate.
If the claimed land is unregistered then notices are usually served on adjoining landowners.
Once the OS Report is provided then referral to a senior technician happens asap due to expedite status and it's for them to decide if more is needed from the conveyancer and/or if notices are then required
Your conveyancer should be aware of the process and hopefully have their own experiences to share. They will also be the first to know/able to check if more is needed and/or notices are served
Practice guide 5: adverse possession of (1) unregistered land and (2) registered land where a right to be registered was acquired before 13 October 2003 - GOV.UK