I have a Vigor2710n and I am using port redirection for basic public access to some of my devices over the Internet. This all works well.
What I require is a method of being alerted (via email) whenever somebody accesses the relevant public addresses and ports.
Can this be achieved by using rules or other approaches?

No.

It can be achieved with a separate syslog server, but the router itself is not designed to send alerts for normal functions like access to a port forward.

With a separate syslog server, you could set up a keyword notification for this text, which is sent when something connects to a NAT > Port Redirection: "Virtual Server: [remote IP]:6625 -> [local IP]:80 (TCP) Web"