Based on the information you have provided in the question and the response to my comment, you have a couple of different options or at least some additional things to think about.
First scenario: Your website and application are hosted on 2 different servers with the URLs of www.companyname.com and www.companyname.com/application. In order for this to work, you will need some type of reverse proxy to send traffic for .../application to the server in South Africa. If SSL is to be used, that SSL certificate will need to reside on your server in the UK on the www.companyname.com site. It gets a bit more complicated if you also want the traffic between your reverse proxy and the server in South Africa to be encrypted traffic. Unless you have the infrastructure to support it, a reverse proxy might not be the right choice for your situation.
Second scenario: Your website and application are on 2 different URLs (www.companyname.com and application.companyname.com). In this scenario there are a couple of different SSL certificates you could use. The first would be a wildcard certificate for *.companyname.com which would then cover any websites under that domain. The wildcard certificate would then be installed on the server in the UK as well as the server in South Africa and still work fine. There is another type of certificate called a SAN certificate that allows you to specify multiple domains in the certificate. For your situation you could have 'www.companyname.com' and 'application.companyname.com' explicitly specified in the certificate. That certificate would then be installed on both servers.
The drawback to a SAN certificate is that you are limited to the websites that you have specified in the certificate, but they cost a bit less. With a wildcard certificate you can specify any number of subdomains and still be able to use the same certificate, but these may cost a bit more.
The other option of course it to purchase a single domain certificate for www.companyname.com and one for application.companyname.com and install on their respective servers. Depending on the SSL provider that you use, this might be the least costly option, but then you have different certificates you would have to manage.
Hope that helps to give you some options.