Thanks Royho for your reply.
We're actually using our own private SSL: secure.mydomain.com
Our main website is on http://www.mydomain.com
I have followed your recommendation of using the wp-https plugin, which seems to work very well. Using the "URL Filters" functionality in wp-https I was able to to setup "/checkout/", "/my-account/", "/order-tracking/", "/cart/" etc for WooCommerce's shop pages.
I have also disabled "Force SSL" in the WooCommerce plug-in as it was suggested on WooCommerce's Known Conflicts page (http://wcdocs.woothemes.com/codex/integration/known-conflicts/#section-4) that this would interfere with wp-https.
When placing items/products into WooCommerce's shopping cart and then clicking on Checkout, this seems to cause WooCommerce to 'lose' the products in the cart after it transfers to the secure cart page.
Any ideas? Your help so far has been appreciated.