From personal experience I am a bit biased against Contact Form 7, but I think Gravity Forms would be the easy solution.
You could link your enquire buttons to the form with the current event (post) id passed as a variable in the URL. So instead of linking like this http://mysite.com/my-form you would just change the link to something like this http://mysite.com/my-form?event=210.
Next, you just create a function in your active theme's functions.php file that hooks into Gravity Forms and passes the value from the URL to Gravity Forms.
Finally, anytime you want to use that URL parameter as a value in your form, just check the 'Dynamically populate this field' check box in Gravity Forms and enter the name of the variable you setup.
Gravity Forms is really slick and I don't setup a site without it. It is about 1,000 times easier to work with than Contact Form 7 and is extremely flexible when it comes to more advanced configurations like you are looking for.