Sorry, I should have written my question more clearly I didn't mean that I thought the plugin was responsible for the problems. I wasn't sure where the problem was originating from and was just asking the question to make sure there was nothing I was missing with regard to setup etc with the Contact Form 7 - Campaign Monitor Addon plugin.
It was as a result of not having Akismet installed. I didn't realise (yes I know, dumb) that the subscription form was so susceptible to spam. I have another site (Drupal) which has absolutely no problems at all with the subscription form. We didn't install Akismet because the monthly cost is almost half the hosting cost and for a small business website it makes my services not competitive compared to other web options in our area - I either have to drop my hosting fee and basically pay for Askismet myself or miss out on the work.