How do we stop International Shipping showing as default?

Can you reproduce it on demand, or does it seem to happen 'randomly'?

Once International Shipping occurs it remains for all. Tried clearing the cache locally and on the server. Tried incognito sessions too but it still returns International Shipping until you enter the delivery address then it recalculates.
The fear is that customers abandon their cart when faced with a £14.99 delivery charge. In reality delivery may be free if they progress and earlier there is the "calculate delivery" button where they can get an accurate cost, but that relies on the customer taking action and many will fail to do so.
The best option it to state "calculated at checkout" but I just cannot get that to re-appear. There must be something that is causing International Shipping to show as the default but i cannot see what.

As mentioned above, the "Calculated during checkout" is normal when either:
a) there is only one shipping method available
b) no prior checkout was done were a method selection was made and then the user went back to cart.  (Which could be cached over a long period.)

So, if you've tested with incognito browser and get the same result, then something's going on that needs to be troubleshooted.  Do you get the same results in your 'development PC' / Visual Studio so that you can debug?

Alternately, I can suggest that you install the Shipping Director plugin.   With Shipping Director, you can set up a rule that would send tracing information to the System Log.  And then set up simple rules that call your existing shipping provider plugins.  
Boolean     $Debug    true
Option       Shipping   true    Shipping.FixedByWeightByTotal
Option       Shipping   true    Shipping.ClickAndCollect
(Make Shipping Director the only "Active" shipping provider plugin.)

Then when you go to the cart, you can check the logged messages to see what was returned.
If interested, contact me and I'll send you a temporary license for your store URL.

Thank you, but unfortunately for this site I run motorcycle tours and will now be tied up on that through to 23rd June. I doubt anyone at the firm will want to undertake this in my absense.