UK VAT at 20% is for UK/EU shipping addresses (applied at the checkout stage). For non-EU shipping addresses, VAT will automatically zero-rate (0%) during the checkout stage (for example, VAT will not be charged if your shipping address is in the USA, Canada, Switzerland, New Zealand and so on).
VAT registered EU companies outside the UK that wish to zero-rate should contact us before ordering, supplying their VAT number so that invoicing and sale can be done manually. The following information is also required: name of contact, company name, billing address, shipping address, telephone number and company email address. If your shipping address is outside the EU, then you don’t need to do this; you can order through the site, with zero rate VAT. You can also order through the website; include your VAT number in the custom notes textbox on the checkout page. The checkout will mention VAT, but the invoice for wire transfer (sent to you after verifying the VAT number with VIES) will remove this and apply 0% UK VAT.
The prices shown on the product pages do not include VAT, because the UK zero rate (0% VAT) applies to non-EU shipping addresses, while the standard UK rate (20% VAT) applies to EU shipping addresses; there is no reliable way for the website to detect whether the zero rate or standard rate of VAT should apply, until the customer has entered their shipping address, so zero rate is assumed until indicated otherwise. The standard UK rate of VAT is shown automatically on the checkout page, if applicable, once the shipping address has been entered.
More information about this can be found at https://www.gov.uk/starting-to-export.