Presumably Amazon have some stats of how frequently each type of card is used on their platform, even if that's just aggregation done on the first 4 digits of the card number.
They are probably well placed to determine how many customers use Visa with them versus Mastercard, or even have both and use both on the website. The subset who have only ever used Visa on Amazon may or may not have an alternative card they could use, but they will presumably have factored in the cost of potentially losing the sale entirely as a result of refusing Visa.
With Visa so entrenched in UK finance, it's not going to be received by customers the same way as Amex being refused (let's face it, Amex is refused most places because the only people who use it do so because they are getting cashback which is paid for by the merchant having increased fees). Instead, Visa will be the card they've always used, so if Amazon stop accepting it, I think a lot of customers will just shop elsewhere instead.
If everyone using Visa credit cards stop buying on Amazon starting 19th January, Amazon will probably budge.
But since everyone has a debit card Amazon must be betting that if they do stop accepting Visa credit cards then customers will just shrug and switch card because they really, really need that stuff now.
