Margaret - our PG 40 supplement section 4 sets out the guidance on how a determined boundary application should be made and the registration process -
Boundary agreements and determined boundaries (PG40s4) - GOV.UK
You will see that there are a number of factors involved one of which whether all the affected landowners have signed/provided consents. Every application is treated on merit and if no such signature/consents are included then decisions have to be made as appropriate - in many cases we may for example request that the neighbour does sign the form/consent but if they won;t then that's the answer to provide. A decision will then be made re next steps as appropriate and as per the guidance linked to