As you state correctly there is a legal requirement to issue a VAT invoice by a VAT registered supplier to a VAT registered customer. The guidance states :
'A VAT invoice is a document containing certain information about what you’re supplying. Paragraph 16.3 sets out the information you need to show. Your customers need VAT invoices as evidence for reclaiming, as input tax, the VAT you have charged them.'
You do not, therefore, have to issue VAT invoices for zero-rated supplies.
You do not need to issue VAT invoices for supplies to customers who are not VAT registered. In practice, this will probably mean issuing a VAT invoice to any customers who ask for one, as you will usually have no way of telling whether they’re VAT registered or not. You do not have to check that a customer is VAT registered before issuing a VAT invoice.
If the suppliers are refusing to meet their invoicing obligations then I would recommend you reminding them again what their obligations are. These obligations are described here:
However this would be a third party issue between you and the supplier and HMRC would not get involved in this type of situation. Again I would speak to the supplier and advise them that you have spoken to HMRC who are in agreement about their invoicing obligation. Beyond this however, we would have to say that it is an issue between you and the supplier and you may seek a legal route if that is required.