This depends entirely on your target audience. There are two trains of thoughts, but both have ultimately the same outcome:
Tell them there and then on the product page.
Audiences who pay VAT
Most consumers will not want to be surprised by VAT at the checkout (it is a hidden cost) and yes this would definitely reduce the number of abandoned carts.
Audiences who do not pay VAT
Simply: how will they know if that is the price they will pay - it may make it cheaper. So even if your headline price is without VAT (which is ok if your audience won't pay VAT) make sure you make it clear there that it is free from VAT. Also worth noting that telling a user once when they enter the site is not good UX - remove it from there and place it where users will be expecting to see it.
Lead with your headline price, but always say "includes VAT at 20%" or "+VAT at 20% = £42".
You can of course vary this. For example if you have business accounts, show with VAT by default, but if they are logged in, show without VAT by default.
Lastly our geographical placement is important - some countries - require you to display the price with VAT/taxes. Waiting until they reach the checkout may actually break certain regulations.