I've worked this out now. Here is the solution, which is rather straightforward. I should have seen it sooner:
ProxyCommand ssh accessable.server nc %h %p
'B' is the Proxy server that you are jumping through. It should be configured as you normally would configure access to a server.
'C' is the destination host. It needs to be configured to use 'B' in the connection process. The identity file in 'C' is the path to the ssh-key on 'B'. The ProxyCommand uses Netcat to open the connection to 'C' from 'B'. Netcat, or nc, will need to be installed on 'B'.
Hope this helps others.