No! As long as postage stamps are bought/sold for their face value or less, no VAT is payable. For further details visit https://www.gov.uk/search?q=postage+stamps

In February 2022, Royal Mail introduced barcodes to stamps for regular ‘everyday’ Definitive stamps. These are the 'Machin' style stamps with just the head of the monarch on them. Non-barcoded definitive stamps are no longer valid for use. However, Special/Comemmorative Stamps with pictures on them, and Christmas Stamps without a barcode, will continue to be valid for postage. We only sell these stamps, which are 100% valid for postage. For further details visit https://www.royalmail.com/sending/barcoded-stamps