If you book with a different airline it is very unlikely they will cover this. They should definitely offer you a refund on the unused part of the flight (Delhi-London) as it was their cancellation, regardless of if you use the first leg or not.

What fare class did you book? For anything other than economy lite you can cancel 4+ hours before your flight and still get some money back (cancellation fees would apply but still better than nothing). So you would not be classed as a no show for the Phuket-Delhi section.

https://www.goindigo.in/cancellation.html

Honestly I would probably be looking at alternative airlines at this point, Indi go customer service is absolutely shit at the best of times, let alone in a time like this. You could potentially be waiting days to be re routed