When Henry VII entered London, he not only started a new dynasty, but he immediately started to intervene in the old dynasties to make sure that they didn’t challenge his new position.
Proclaimed King of England by Sir William Stanley, he was as yet unmarried to Elizabeth of York, the to-be mother of Henry VIII. Instead, he stayed with the Queen Mother, also confusingly named Elizabeth. (Seriously, everytime I get to that bit in Richard III when he’s wooing Elizabeth, I have to apologize that they used so few names back in the medieval/early modern periods.)
Nineteen year old Elizabeth of York was housed at Coldharbour House, along with the eight year old Duke of Buckingham and the ten year old Earl of Warwick. Coldharbour House was granted by Henry VII to Margaret Beaufort, who then went on to arrange marriage between Thomas Grey and Eleanor St. John, neutralizing the Grey’s opposition to the new dynasty. Further, Margaret Beaufort took into her custody the surviving heiress of the York house, Cecily of York.
Within the next few months, working with his mother and his close allies, Henry VII ensured that the families who had been so influential in the previous decades, the Greys, the de Veres, the Stanleys, would be firmly on his side.