Shortlist: (top 2 = Shanaya or Serena)
Shanaya (pronounced SHA-NAAA-YA, like Shania Twain), the spelling Shanaya is the Indian spelling
Serena
Elina/ Eliana (saw these on another thread and think they're quite pretty and Indian-sounding), similar to the Indian names Leena, Leela and Ila but different.
As a wild one... we quite like Larissa (totally unrelated to our culture but we like the name and it is our Western name option incase we decide to go for a completely western name. Would this suit a British Indian baby or is it too Greek/Russian?)
The ones we ruled out thanks to all of your wonderful and helpful comments:
Jiya (sounds like jeer)
Ruhi/ Rohini/ Ruhani (not international enough, too old school for us)
Maya (overused and a bit bland for us)
Siya (sounds like see-ya later)
Ananya (sounds like a-nun)
Aria (masculine name in some cultures, harsh sounds to our ears)
Leela (too simple as a first name and overly common in India, parents not keen on it)
Anushka and Anya (too harsh sounding)