The VAT Guide (Notice 700) now includes an invalid invoice guide, in section 16.8.
This is quite helpful, as it indicates the type of alternative evidence which HMRC would accept if you are unable to obtain an invoice from a supplier.
The list of conditions in para 16.8.1 is helpful, as is the types of evidence in para 16.8.3.
But, don’t let this wording create a quasi-law. HMRC discretion is exactly that. In some cases, there will be plenty of evidence but HMRC might choose not to exercise their discretion in allowing the input tax claim. In other cases, there may be very limited evidence, but HMRC will allow the claim. It depends on their review of the evidence provided and any cross-checks they might make.
The wording suggests that the taxpayer should routinely send their evidence to HMRC for review. If every taxpayer who received an invalid invoice were to do this, HMRC would quickly be inundated.
My approach is to be quite selective on which invoices require HMRC discretion. In particular if the value of input tax at stake is unusually high.
This discretion is provided by VAT Regulation 29(2).
Do note that an appeal against a decision of HMRC not to exercise their discretion must be based on whether HMRC have been unreasonable in not allowing the claim.