I'm surprised to say... that SSL certificate you have is very poor quality and has a number of pretty significant security issues, in addition to the SHA-1 encryption.]
To answer your specific question, there's nothing you or your devs can do about the SHA-1 encryption problem, as that problem exists on one of the certificates in the chain that is owned and controlled by Thawte (the cert issuer or "Certificate Authority"), not your own certificate. It is up to them to fix it.
As you can see from the cert security scan, there are a number of other issues with the certificate that are unacceptable. Especially in a paid certificate. [Edited for clarity - some of those warnings are likely server-specific, meaning the server is being allowed to communicate with certificate in less than optimal ways]
https://www.ssllabs.com/ssltest/analyze.html?d=www.key.co.uk
It's unlikely that the encryption problem is whats giving the "not secure" warning on the site at the moment (although it will become a major issue later in February) so you'll need to keep looking for resources called over HTTP if you're still getting warnings.
When I had a quick look at the home page, I didn't see any more warnings, as it appears you've fixed the image call that Andrew mentioned. You can use Chrome or Firefox Dev Tools to inspect any pages that are not secure to be shown exactly what element is causing the failure. It often comes down to hardcoded images like those in CSS/background images etc, or hardcoded scripts. For example, your Quotations page is calling a script from Microsoft to validate the form, but it's failing as it's called over HTTP.
Knowing this, you'd want to check any other pages using such form validation. A thorough Screaming Frog crawl to look for any other wayward HTTP calls can also help dig our the remaining random culprits.
Hope that helps?
Paul
Sidenote: Your certificate authority is Thawte, which is connected with Symantec. Which has done such a bad job of securing their certificates that Chrome and other browsers no longer trust them and are in the near future are going to be officially distrusted and ignored. Symantec has in fact given up their Certificate Authority status and is transferring their business to a new company which does have a trusted infrastructure for issuing certificates. So you're going to need to deal with a new certificate in the not too distant future anyway.
Given the poor security of your existing cert, and the upcoming issues, if it were me, I'd be asking for a refund of my current cert, and replacing it with one from a more reliable issuer. I know that can mean a lot of extra work, but as these existing problematic certs go through the distrust process over the next 8 months, sites that haven't dealt with the issue are going to break.
It's possible that Thawte will build out a reliable process for migrating. At the very least, you need to have a strong conversation with your issuer about how to insure you are getting the security and long-term reliability you've paid for. Sorry to be the bearer of bad news that is a much bigger issue. You can read up about it more here:
https://security.googleblog.com/2017/09/chromes-plan-to-distrust-symantec.html