There has been no specific customisation to the checkout. There are plugins such as 7Spikes One Page Checkout and Klarna Checkout but nothing in those should be causing this. In the 7Spikes plugin the default billing and shipping country is United Kingdom. It also has “Preselect Last Customer Shipping Address” but again this would only impact with a known user whereas International Shipping is appearing as default even with an in-private session.
This problem is still unresolved. Try visiting https://www.westcoastharleyshop.co.uk/ pop something into your basket and go to checkout and you will see what I mean.
I agree that the plugin looks like the culprit but the client wants this suite of plugins left in place. What is bizarre is that the results are inconsistent. Some see International Shipping at £14.99 whilst other see it is to be calculated at checkout.
I was just suggesting that you turn it off temporarily, or in a test system, to prove that it is the plugin. Then you could open a support ticket with the plugin vendor.
I thought this problem was resolved but is seems not. It is the strangest thing because no settings appear to have changed yet the values presented have. Last time I successfully got the cart to return:
Shipping: Calculated during checkout
However, on checking another matter today I was presented with: