Very very indirectly. They are both descendants of John of Gaunt, so they are descent cousins.
John of Gaunt+
1.Constance of Castile
Katherine of Lancaster-Henry III of Castile
John II of Castile-Isabel of Portugal
Isabella of Castile
2. Blanche of Lancaster
Philippa of Lancaster-John I of Portugal
Infante Joao of Portugal-Isabel of Bragnanza
Isabelle of Portugal-John II of Castile
3. Katherine Swynford (mistress of John of Gaunt whom he married in 1396)
John Beaufort-Margaret Holland
John Beaufort-Margaret Beauchamp
Margaret Beaufort-Edmund Tudor
Henry (VII) Tudor-Elizabeth of York
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