The provided source material does not contain any information related to free samples, promotional offers, no-cost product trials, brand freebies, or mail-in sample programmes. The sources exclusively discuss indoor activities in London suitable for rainy weather, such as museum visits, gallery exhibitions, and other cultural or entertainment options. As there is no data on the requested topic, a comprehensive article on free samples and promotional offers cannot be written based on the provided documents.
Conclusion
The source material provided is focused on rainy-day activities in London and does not include any factual claims, details, or information regarding free samples, promotional offers, no-cost product trials, brand freebies, or mail-in sample programmes. Therefore, it is not possible to produce an article on the requested topic using only the provided sources.