I 'think' I have figured out how to fix my problem so will explain what I did in the hope it can help you.
First of all, the issue was related to the email subscription form which was created using the Campaign Monitor addon. There is no captcha on the form which means that spam bots can invade.
The emails were blank because I had no information entered in the Mail fields (except the clients email). As soon as I entered information such as [your-name] <[your-email]> in the from field and something in the Subject field the spammy emails had a from name... still no subject.
I then set up Askismet which I think is what has actually solved the problem.
In your case, if you are experiencing problems with the contact form only it might be because you don't have the captcha enabled.
Also, check to see what information you have entered in the Mail fields (group of fields below the form fields). If you don't have [your-name] <[your-email]> in the From field any enquiries you get will say they are from wordpress.
Am still not 100% that the problem has been fixed - still monitoring the situation.