As the anti-vaccination movement is spreading around the world, this paper addresses the ever more urgent need for health professionals, communicators and policy-makers to grasp the nature of vaccine mis/disinformation on social media. A one-by-one coding of 4511 vaccine-related tweets posted from the UK in 2019 resulted in 334 anti-vaccine tweets. Our analysis shows that (a) anti-vaccine tweeters are quite active and widely networked users on their own; (b) anti-vaccine messages tend to focus on the "harmful" nature of vaccination, based mostly on personal experience, values and beliefs rather than hard facts; (c) anonymity does not make a difference to the types of posted anti-vaccine content, but does so in terms of the volume of such content. Communication initiatives against anti-vaccination should (a) work closely with technological platforms to tackle anonymous anti-vaccine tweets; (b) focus efforts on mis/disinformation in three major arears (in order of importance): the medical nature of vaccines, the belief that vaccination is a tool of manipulation and control for money and power, and the "freedom of health choice" discourse against mandatory vaccination; and (c) go beyond common factual measures-such as detecting, labelling or removing fake news-to address emotions induced by personal memories, values and beliefs.