cart problems

We are having problems with cart.
After adding a product to the cart and then deleting that product, returning to product listing page, then adding another item to cart and going to checkout, the previous item is still showing up as still being in the cart.
Any suggestions as to how to resolve this please.

Jane

Hi Nicholas,
here is our website address

www.simplyexquisitejewels.co.uk/

click on product listing, then add items to cart from one of the menu headings

We did have multicart enabled, have disabled that and are still getting the same problem.
We have just changed hosts from Hostpapa to Siteground, so thought we should do a test purchase, this is when we noticed the problem.
We are not using the same products for the test.
This is how problem is generated, click product listing, then any menu header, add a product to the cart, then go to checkout and,delete the product giving an empty cart. Add another product to the cart, go to checkout again and the first product deleted is still in the cart.
At times the delete button is not working and there is no delete button in the cart, even though it is enabled.