Modi arrived at the Buckingham Palace in a Jaguar - built by the Jaguar Land Rover (JLR) - on the second day of his maiden three-day visit to the UK.
Earlier, a visit to the factory of Tata Motors-owned JLR in the West Midlands region was said likely to be squeezed in, based on availability of time.
The 89-year-old Queen greeted Modi at the Grand Entrance of her London palace, shaking hands with him before they moved on to inspect items from the Royal Collection, brought out specially for the Indian Prime Minister's visit.
Soon after the lunch, Modi will head to the iconic Wembley Stadium to address a 60,000-strong audience at the 'UK Welcomes Modi' event.
Yesterday, India and the UK announced deals worth 9- billion pound as they inked a civil nuclear pact and decided to collaborate in defence and cyber security besides launching a railway rupee bond in London market.