Henry's father, Edmund Tudor (half-brother of Henry VI), had no claim to the English Throne at all; he was the son of Catherine, the widow of Henry V, who had remarried a Welsh gentlemen, Owen Tudor
The system of political and social organisation in medieval Europe, in which society was organised into a strict hierarchy with the monarch at the top, and where land was held in exchange for military service
Henry couldn't count on the support of Lord Thomas Stanley (his mother's husband) or his brother Sir William Stanley who had promised to use their 3,000 troops on Henry's side during the battle
Henry replaced Richard III who had been widely disliked (although he had more popularity in the North) and the belief he had murdered his nephews split the Yorkist cause (Anti Ricardian Yorkists such as the Woodvilles)
Lambert Simnel, thought to be the son of an organ maker, at the age of 10 was used by his patron Richard Symonds (a priest) and the Yorkists, to impersonate Richard of York