The royal couple are also visiting Waltham Forest and Harrow.
Tory leader of Redbridge Council Keith Prince said the Queen's visit was a "great privilege and honour".
When the royal couple first arrived, they were greeted with a huge cheer and the Queen and duke walked along a path to the mansion stopping briefly to meet some of the well-wishers.
Some of the residents welcomed the Queen by decorating their houses with large flags and bunting, hung from rooftops.
'Good humour' Philip showed that despite his recent health problems he had lost none of his blunt sense of humour when he joked with a disabled man about his mode of transport.
He walked up to David Miller, 60, and gesturing to the four-wheeled mobility scooter he was sitting on, he asked "how many people have you knocked over this morning on that thing?".
Mr Miller, a trustee of a charitable trust that runs the Valentine mansion, has difficulties walking, due to a spinal problem.
At the 17th Century house, they viewed paintings by artists including Lucian Freud, Francis Bacon and David Hockney.
As the Queen left the building, she came across artist Jason Rose painting a portrait of his teenage son in the lobby.
She asked his son if he had a day off school and when he said he did, she asked: "Why are you wearing your school uniform?"
The 14-year-old made her laugh when he said: "I managed to get the day off because I told them I would wear my uniform."
Catering courses Before leaving, the Queen opened Valentines Diamond Jubilee Dry Garden - laid with plants that need little watering - surrounded by cheering crowds.
The Queen and duke then went to Walthamstow Assembly Hall for a lunch attended by mayors from the 32 boroughs and the City of London.
The silver service lunch was prepared by Indian chef Cyrus Todiwala, assisted by cooks from top London hotels and served by students from catering courses from across the capital.
Business leaders, community workers and religious leaders also dined.
In Harrow, the royal couple were going to the Krishna Avanti School where were viewing dance and musical performances by schoolchildren and local groups.