“Jumping in too

.. Should I leave my website as it is then with all products being http but sign up, log in and payment sections being https..”
To be honest Andy, that doesn't make much sense. If you have already gone to the expense of a certificate and are already using https for part of your site, you might as well use it for all of your site and get any associated benefits. But as above don't suddenly just redirect everything.
To make your site www.pewterworld.co.uk fully https, you have a bit of work to do as you are currently in a halfway house. eg you can access your home page as https://www.pewterworld.co.uk/
But the rest of your site isn't ready as you have content on your pages which is pulling from a non secure source eg:
https://www.pewterworld.co.uk/Jewellery/Pendants/Celtic-Heart-Pendant-1
This page is insecure as it it references an image that is specifically coming from a http source:

The source of this is: http://www.pewterworld.co.uk/images/Delivery/4-7days.JPG
To fix this, you would instead just reference: /images/Delivery/4-7days.JPG
So you would need to make sure any absolute paths that point to http sources are changed for all of your product pages and the whole website.
You already have the canonical tag, eg:
<link rel="canonical" href="http://www.pewterworld.co.uk/Jewellery/Pendants/Celtic-Heart-Pendant-1" />
So when ready, change this from http to https.
Once you were happy Google had re-indexed all of your pages as https, you can then redirect all of your pages to https.
Obviously this is my fag packet research, so although I don't think it would be a big deal for you to move fully to https, don't go and implement a site wide https plan based on this post
Make sure you sit down and plan it properly with your hosting partner/web bod.
Remember the 6 P's - Proper Planning Prevents P*** Poor Performance 