"As millions of people mark this important milestone we can reflect on the enduring and special relationship between our two nations - the world's oldest democracy and its largest," Cameron said in a statement from Downing Street.
"This relationship has gone through great changes. Our collaboration is now stronger, deeper and more far-reaching. It is a partnership between two equals with a mutual respect for each other," he added.
"On my recent visit to India I was reminded of the continuing strength and unique warmth of the very special relationship between our two countries."
He went on to highlight how Britain would not be the same without the extraordinary contribution of the Indian diaspora in business, cultural and sporting life.
"So let us celebrate this important day together, as two like-minded democratic nations whose bond of friendship grows stronger every year," he added.
"The Republic Day celebrations remind us all of the strong and deep ties between our people and our governments and the importance of the partnership between the UK and India: the oldest and largest democracies in the world," she said in a statement.
"India is important to the UK - the Prime Minister (Cameron) has made clear that he accords 'top priority' to India. I am proud to say that the UK-India relationship has never been better," she added.
"The much-anticipated statue of Gandhi in London's Parliament Square in London will also carry huge resonance in both our nations and across the world.
The Prime Minister has also personally invited Indian Prime Minister Narendra Modi to visit the UK, where I know that he will receive an especially warm welcome from the diaspora community," she said.
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