You could remove the standard Magento shipping quote altogether and have a drop down menu so that customers could see all (one) of the shipping options straight away on the basket page. I downloaded and installed this extension and it worked well.
Make sure your default country is United Kingdom in system > config > general
To remove the standard shipping option copy of the following file to your local folder: template/checkout/cart.html and look for the following line:
getIsVirtual()): echo $this->getChildHtml('shipping'); endif; ?>Then comment it out.