The law on this is quite simple: While the retailer is not required to proactively offer VAT invoices to non-VAT-registered customers, If a customer requests a VAT invoice the retailer HAS to supply it - there is NO requirement for that customer to be a VAT registered business and the retailer has NO legal right to dispute the request.
This rule can be clearly found in HMRC's publically available "VAT Notice 700/21", in paragraph 4.4, and in the various other VAT instructional documents issued when a business registers to become a VAT charging supplier.
When asked for VAT invoices EE chooses to "force" customers to register as business accounts so they can justify charging them more, as the business tariffs are more expensive and don't include as many freebies.
To the letter of the law, EE are in contravention of VAT Notice 700/21 by refusing to provide a VAT invoice without caveat, and if you argue that to them they will probably set your account to receive VAT invoices without further argument. I did this several years ago (successfully) but I have noticed the VAT breakdown and VAT number have surreptitiously dropped off my monthly bills!
