From the Purchaser Manual, as part of the Law Consumers Society Conveyancing Kit as purchased in 2017:
The enquiries which must be ordered by a purchaser are: Section 603 certificate from the local council for outstanding rates on the land Section 66 from the water authority for outstanding water rates Section 47 from the OSR for outstanding land tax, go to 4.07 for more detail
Section 4.07 is rather wordy so I wont quote it here, but says same thing.
I just looked at the Vendor disclosure section and there is nothing on land tax there. Its too bulky to copy here, however.
Its a valid point about privacy, but when you think about it I can (and in a conveyancing situation, must) do a title search on the vendors property, which reveals information no less private. Therefore, if I have the address on any property I can do a title search and find out owners, finance details, caveats etc.
Of course theres nothing stopping a vendor getting a land tax cert, and handing it to the purchaser, but a prudent purchaser would still do the search anyway. What I meant by mindset. Rely on your own enquiries, and end up with no regrets.