On the mortgage point, a HIP is irrelevant.
Most lenders require searches (local and drainage, possibly environmental, coal if required and any specialist as appropriate eg Cheshire Brine, Cornwall Tin) which are under 3 months old at completion.
Indemnity insurance may be an option though, depending on the lender, for no or out of date searches (HIP searches can be 12 months old but most lenders require them to be under 3 months old at completion).
In any event, if there is no requirement to provide a HIP, the liability for searches and the costs (save the EPC) lies with the buyer.