Japan Centre Address - in the basement
Product - photo and description - 500mls for 4.36GBP - makes 4.5 litres

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There's also the Rice Wine Shop at 82 Brewer Street (also near Picaddilly Circus) - it costs 3.99GBP here
MAP
http://www.ricewineshop.com - this shop is open until 9pm, sometimes later.

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And on the same street, but further to the East, towards Soho is the Arigato Supermarket
http://www.allinlondon.co.uk/directory/1162/20658.php - 48-50 Brewer Street.
It's likely to be a little more expensive here than at the Rice Wine Shop.

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It's likely to be labelled Calpico rather than Calpis