Inspired by human fact checkers, who use different types of evidence (e.g. tables, images, audio) in addition to text, several datasets with tabular evidence data have been released in recent years. Whilst the datasets encourage research on table fact-checking, they rely on information from restricted data sources, such as Wikipedia for creating claims and extracting evidence data, making the fact-checking process different from the real-world process used by fact checkers. In this paper, we introduce PubHealthTab, a table fact-checking dataset based on real-world public health claims and noisy evidence tables from sources similar to those used by real fact checkers. We outline our approach for collecting evidence data from various websites and present an in-depth analysis of our dataset. Finally, we evaluate state-of-theart table representation and pre-trained models fine-tuned on our dataset, achieving an overall F1 score of 0.73.