Calculating CGT on shares gifted from spouse’s S104 holding

Hi I own a number of shares in one company, acquired over a few years at various different dates via an ESPP scheme and RSU grants. I would like to gift some of these shares to my wife and am slightly confused as to how she should calculate the CGT if she then sells her shares. What would be considered her cost basis for these shares? The advice seems to be "Their gain will be calculated on the difference in value between when you first owned the asset and when they disposed of it", but that seems illogical given that my own CGT calculations are not based on the value of individual shares when I first acquired them, but on the average acquistion price of all my shares in that company — as determined by the S104 calculation. For CGT purposes, would my wife actually be considered to have acquired the shares at my S104 average price on the date I transferred them to her?

Hi
There is no capital gains tax liability on the transfer of assets between spouses or civil partners.  
Your wife would use the cost of the share when you acquired them or the S104 value, to work out any gains if she sells the shares.
Thankyou.