I am aware of tools such as mailchimp but are there any very simple ones? (free of course)
Of course it means you need to setup Sendy. I was going to setup as Sendy as a Service business, but most of the money would be paying license costs for software I could easily build with enough time, so I canned the idea and focussed on other projects.
It's simplistic and doesn't have all the features that MailChimp offers, but it is way more intuitiv and cheaper once your audience scales.