Do Origin do phone only? If they don't it may be that Origin will be ceasing everything because of BTOR ceasing the broadband.
You have a valid point there and one that makes the most sense. Origin use several suppliers, in the OP's case it looks like they are using PN. I don't think either Plusnet or Vodafone (one of their other suppliers) do landline only.
Although Origin do have their own network covering parts of Yorkshire and as such are Openreach customers... in this particular case communication may have been further complicated by the fact its Origin > PN > BTw > Openreach and why there is some confusion.
The OP may need to find a carrier who is prepared to take over landline only - such as either BT consumer or Pulse8.
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ETA
The OP needs to ask Origin if they do WLR (Wholesale Line Rental) so they can provision phone line only services. If they don't - and I suspect they don't because I cant see anything on their site which indicates they do - then you must tell them that you do NOT want the phone line ceasing and that you wish to transfer your line to another service provider.
It's worth pointing out that cancelling broadband on a phone line may attract a cease fee. Look out for both this and any early termination fees. In this particular case you should not be responsible for a DSL cease fee.
If you do need to migrate to another carrier I'd also argue any early termination fees because this is not your fault. If Origin can't provide you with WLR, then it's up to Origin to recoup any Openreach charges and/or any fees that may be passed on by their supplier.