Halifax will charge you a minimum of 12.9% APR for any cash withdrawal you make at home or abroad using the Clarity card so add that charge to your calculations.
In addition, MasterCard (not Halifax) will create the exchange rate that you pay from a collection of sources including Bloomberg, Reuters and central banks and this will "generally reflect" wholesale rates. You can check this in the Halifax T&Cs. However, it not be interbank rates as Mastercard will be creating a margin for themselves on each transaction. Even a tiny percentage margin on the millions of transactions each day adds up to large profits. That's what MasterCard do, they either charge you or the retailer to make their money.
There are many ways to minimise the charge you pay for FOREX and huge savings can be made depending on who you go to ( and their margin) and how much you are changing. You can even hedge against the currency moving against you if you operate in multi currencies regularly.
But as this isn't the standard 2 weeks in Turkey tourists situation then my original post seems to offer a decent balance between convenience and costs.