Hello Olivia - the first thing to establish is what do they mean by 'split out'? Do they mean that they are claiming ownership of the land? The neighbours are transferring it to them? Or something else. The answer will give you a better idea of what's required.
As for waiting that isn't an issue as they can request expedition to keep the processing time as short as possible.
Request an expedite - GOV.UK
Expedition isn't a magic wand though so again what the actual application is for will have a bearing on how long the wait might be. For example a claim could be 3-4 months at least whilst a transfer might be a few weeks. Everything depends on everything being submitted correctly of course though
Suggest you speak to your own conveyancer/the seller to confirm precisely what's happening and when they expect to submit the application and ensure that they also request expedition
And if they've submitted it already ask them to confirm the title number and our case reference