Introduction to Stamp Duty on shares and Stamp Duty Reserve Tax (SDRT): Stamp duty - payment and penalties: who pays Stamp Duty?
The legislation governing Stamp Duty (SD) does not say who is responsible for paying SD. What it does do is to say that an instrument is not available for any purpose whatsoever other than as evidence in criminal proceedings (SA1891/S14 (4)) unless it has been duly stamped.
In practice, this normally results in a document that needs to be stamped being presented for stamping by the person who wishes to use it. For example, a stock transfer form would normally be presented by the purchaser as he would wish to use it to register his ownership of the shares in question. Likewise, a form 169 evidencing the purchase by a company of its own shares would be presented by the company so that it could discharge its responsibility to register the form at Companies House.
In both of the examples given above the person required to act upon the document (the company registrar and Companies House respectively) will refuse to do so unless the document is stamped appropriately. Further information can be found at STSM016010 and STSM016020.