You can create automations based off the Emails and Activities integration. That would be a good way to populate the data you are looking for. For instance, you could increase a “sent count” every time an email is sent, or create an item when an email is sent to track that action as an activity.
Although you can’t directly increase a number, you could automate a status change and chain that together with a custom automation that resets the status and increases a number.
Thanks for your suggestions, it made me look at the requirements in a different way and realise that we don’t actually want ‘every’ email captured, as not all are adding value. As a work around I created a new activity type ‘Email - lead advancement’ and simply add that activity after sending an email that should be included.
I think that will work for now!