Could a carbon tax be a substitute for VAT? VAT is a tax on consumption. However, while in some instances it taxes negative externalities (e.g. fossil energy consumption) in many other cases it taxes services without externalities or potentially positive externalities (e.g. advisory services on how to reduce carbon emissions).

If consumption is being taxed arguably it would make more sense to tax consumption that actually causes negative externalities. Carbon taxes would be an obvious candidate (though arguably not the only one). The price of a product in a value chain would increase as carbon is added to it, just as with VAT, only that the tax is on "carbon added" rather on "value added".

Presumably a carbon tax would also be easier to administer than a VAT since carbon is taxed only where it enters the economy?
No, taxing externalities is not a good substitute for VAT for several reasons.


Pigovian taxes (taxes on externalities) have to be set up in an optimal way to actually reduce externalities. However, it is astronomically improbable that the same level of tax that mitigates the negative externality is exactly the same level that government has to raise for optimal provision of public goods.
It can be shown that Pigovian taxes can be imposed without deadweight loss on economy (which almost all taxes have) but such result hinges on a fact that they are made revenue neutral - hence to use Pigovian taxes in most efficient manner you should used them in a way that does not raise any additional revenue.
By discouraging the activity that creates negative externality the tax basically by substitution effect erodes its own tax base. Every tax does this to some extent - VAT for example encourage substitution of savings for consumption or substitution away from market goods to non market goods but since VAT is very broad this should reduce tax base much less than just selective tax on goods that create negative externality.


Consequently, Pigovian taxes are ill suited for  raising government revenue. Government should still pursue Pigovian taxes everywhere where there are externalities as correcting the externality is always optimal from social perspective. However, no modern government can realistically raise the kind of money it needs to run itself without VAT - in fact it is no accident that modern governments expanded precisely when modern VAT and income taxes were developed, if you check most government budgets VAT and income tax are always the biggest sections on revenue side of budget.