Right. You're going to have to find the owner to approach them about buying the land.
The difficulty with unregistered land is that the evidence of the title is not centrally held anywhere that you can approach, the evidence of title is the actual historic conveyances from when the property was previously sold and bought. The owner can direct where these deeds are held, or they would have been placed with the lender holding a mortgage over the property.
I would start by asking the owners of the properties nearby if they are aware of who the owner is, if they are not then ask about previous land estates in the area who might have owned it once or would know who does now.
Concurrently you can contact the local authority about the land and ask them to check their records for any land charges or other records indicating ownership. They may cite confidentiality, but you can politely ask them to be an intermediary and contact the owner to make them aware of you interest.
You can also contact other local institutions (eg. solicitor's firms, church, pubs etc) to see if anyone there knows.
Failing all that you could place an advert in the local paper requesting that the owner contact you.
You might also consider performing index map searches of the land registry for adjacent land until you hit upon some that is registered and then approach the owner of that land to see if they have any info. You can do this by submitting Form SIM (available from the LW website) attaching a map with areas edged red.
It might be frustrating I'm afraid.
If this is useful please kindly click accept so that I may be rewarded for my time. It will be gratefully received and you will be free to ask follow up questions.