Modi was hosted for lunch by the 89-year-old Queen on the second day of his maiden three-day official visit to Britain.
"Presented Her Majesty The Queen some photographs taken 54 years ago from her first visit to India in January-February 1961," Modi tweeted about the snaps taken 54 years ago when she visited India to be the Chief Guest at the Republic Day parade in New Delhi.
"Also presented to Her Majesty some award-winning Darjeeling tea from Makaibari tea estate in West Bengal & fine organic honey from J&K. Tanchoi stoles that are a speciality of Varanasi were presented by me to Her Majesty the Queen," the Prime Minister, who is on his maiden visit to the UK, said.
Earlier in the day, Prime Minister Modi gifted his British counterpart David Cameron a specially handcrafted pair of bookends with verses from Bhagavad Gita engraved on it and a book compiling letters sent by Indian soldiers during the World War I when they served in France.
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The centrepiece of each of these bookends is a silver bell which has a verse from the Bhagavad Gita etched in Sanskrit, along with its English meaning along the inside rim.
These verses are taken from Chapter 13 of the Bhagavad Gita.
In view of Cameron's fondness for Robert Graves' work on World War I 'Goodbye to All That', the Prime Minister also presented to him David Omissi's 'Indian Voices of the Great War'.
To First Lady Samantha Cameron, Modi presented Aranmula metal mirror, a unique handicraft from Kerala, and some pashmina stoles.