Hi Jack - what happens next as a buyer is very much a matter for you and your conveyancer to discuss and agree upon although I do appreciate the uncertainty you refer to.
Generally speaking if there is an uncertainty then you bounce that Q into the seller's court to consider and provide answers that hopefully provide the certainty you want.
From a registration perspective there is no uncertainty and perhaps the following helps to explain why.
The title plan, which we map and create, is our certainty re the registered extent/general boundaries. It's not intended to be definitive for example re the precise position of the legal boundaries - see our PG 40 supplements 3 and 5 for guidance -
Land registration: Practice guides - GOV.UK
MapSearch is an online tool provided to business users to enable them to locate a property and identify quickly the title number(s) for that property. It's not meant to be used for anything else as it's the title plan that matters/provides the certainty for actual land registration
And a surveyor's map/report is simply that - a professionals view/interpretation of matters on any plan with the lie of the land and more as appropriate to what their remit, skills etc are
Taking all of that into your considerations the key Q asked of you as a buyer is 'does the property you are buying broadly match what's shown on the title plan or are their any discrepancies you wish to raise?' - if there are, and clearly there are some concerns otherwise why have a survey that provides the plan (and report?) you have, then those concerns are as mentioned for the seller to resolve for you
And if they can't then they need to decide what the issues are and whether an application to amend the registered extent/title plan is warranted bearing in mind the limitations as explained and highlighted in the PGs as mentioned