Unregistered lease from 1935

I think this comes out of desperation ...... we're stuck.
We're selling my mother's  freehold house, offer accepted Oct 6th by first time buyers, a mixture of savings and mortgage.
My parents bought the house in 1964, at that point it was leasehold.
They bought the lease in 1991. My dad died in 2011, my mum is in a care home. We have LPA.
It's now been discovered that there is an unregistered lease from 1935 running for 99 years.
The counterpart is missing.
How likely is it that we're going to lose the sale of our mother's house, if this is not sorted out?
Our solicitors said today they'll be going to the Land Registry.
Please advise us and give us hope, we need that more than anything.

Bernadette - I am sorry to read of your desperation. Such things can be a significant issue for buyers, and sellers, alike and do need to be resolved.
Responsibility for holding the lease/counterpart rests with the landlord/tenant but it is appreciated deeds can go missing, get lost etc. If that's what has happened here then updating the register to remove the noted lease will rely on what evidence you can provide to demonstrate that the noted lease is 'no more' as in the interest created no longer exists as X, Y and X happened for example.
If you can demonstrate that in law then there is always hope that the register can be updated. The buyer will not complete if they are buying with a mortgage in my experience so very much a case of your relying on your legal rep to explain how the law works re such leases and how they can be proven to have been 'determined' depending on the facts you can provide - Practice guide 26: leases – determination - GOV.UK

@Adam Hookway.
Thank you for your detailed reply and outlining the reality of the situation.
That is very helpful.
Our conveyancing solicitors have been extremely helpful and proactive.
It will be going to Land Registry with a plethora of supporting information, so we have to hope that we have a successful outcome.
It's honestly been the most stressful week, particularly as it's our mother's house, the one we grew up in and we're caught up in a legal mess that we had no idea was coming down the line.