Hello Amy - the application was submitted today so it needs to be processed to decide whether it is sufficient to cancel the noted lease. As you are already aware everything depends on the supporting evidence submitted to show that the noted lease no longer affects.
It's less about the house and all about what evidence they provide to show that the lease has come to an end/been determined/no longer effects and as you state they haven't really supplied anything concrete it seems to prove that in law.
They should now apply to expedite it as there is an onward purchase so I shall flag with colleagues to ensure that happens. Expedition generally means it is considered asap and within 2 weeks but everything then hinges on it being in order.
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PG 26 explains how a lease can be determined but it doesn't read as if the conveyancer has applied the guidance. But until their application is considered we can't be definitive re whether it is in order or not.
In the interim, and whilst you wait to find out, I would suggest discussing what options exist with your own solicitor for example an indemnity policy although I suspect that has already been discussed if they have advised you that you cannot complete