Redmine

+1

I think it would be enough like the way the status or any fields are updated by entering the "name: value" at the beginning of the email.
e.g.

Spent time: 1:07

Or like in the commit message @1:07

A default activity should be set, another keyword should be available to explicitly set the activity type, maybe even the log message.
Or a combination of these in one line:

Spent time: Activity_type@hh:mm log_message