Hi Wibble, any gains and losses will be crystallised on sale. To be clear, the 'move' function, although a simplified dashboard process for the account holder, will still go through a sale of asset into cash in the GIA(using this example) and a transfer into the ISA tax wrapper. It is not an in-specie (transfer in its current form) process. Whether there is actual tax to pay will be determined by your individual situation. In summary, this process could trigger a taxable event.
Regards
Adam