which of these groups crossed the english channel for this battle?
Henry Tudor, a descendant of the greatly diminished House of Lancaster crossed the channel.
Battle of Bosworth Field
 Across the English Channel Henry Tudor, a descendant of the greatly diminished House of Lancaster, seized on Richard's difficulties and laid claim to the throne. 
where did the field of fire take place UNANSWERABLE which was the battle associated with the lancastrians? The Battle of Bosworth Field. is this battle known by any other name? Yes, Battle of Bosworth. who was this battle fought between? Between the Houses of Lancaster and York that extended across England in the latter half of the 15th century.
wiki:1600352
Battle of Bosworth Field [SEP] Introduction
Historians consider Bosworth Field to mark the end of the Plantagenet dynasty, making it one of the defining moments of English history. Richard's reign began in 1483 when he seized the throne from his twelve-year-old nephew Edward V. The boy and his younger brother soon disappeared, to the consternation of many, and Richard's support was further eroded by unfounded rumours of his involvement in the death of his wife. Across the English Channel Henry Tudor, a descendant of the greatly diminished House of Lancaster, seized on Richard's difficulties and laid claim to the throne. Henry's first attempt to invade England in 1483 foundered in a storm, but his second arrived unopposed on 7 August 1485 on the southwest coast of Wales.