I have already replied to the point about buying the freehold when you can't find the freeholder here:
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I assume that you have already been down the Land Registry route. If the Land Registry does give information about the freehold then obviously this should be followed up, but the normal difficulty is that the freehold title is not registered. Depending on where it is in the country compulsory registration of title might well not have applied when the freeholder bought the freehold. That is the normal problem with these missing freeholder situations.
As far as the HIP is concerned, this is the kind of case that is going to confuse a HIP company, but a local solicitor with knowledge of the area would probably have met the issue before and would deal with it in a common sense way. This just reinforces the point about finding a good conveyancing solcitor and getting him to arrange the HIP.
As a conveyancing solicitor I believe the information given in the post to be useful but I accept no liability except to fee-paying clients