Upvote:3
This is based on my experience. The ultimate answer would be to call the US consulate in London and ask them.
I think it depends on your visa type in the UK.
I was granted my H1B visa last year as well. I went back to my home country to get my passport stamped and not in the UK. I was working in the UK at the time. If you're only on a business trip in the UK on business visa I don't think you can get your passport stamped because your resident country is still India. However, if you're working in the UK and you can prove that you're a resident in the UK then I think it's ok to get your passport stamped in London.
Please do confirm with the US consulate in London.
All H1B visa stamps must be issued by the U.S. consulate outside the USA. To be more precise, H1B visa stamping must be obtained from the US consulate situated in your home country.
Re-stamping of H1B Visa: If you currently hold H1B work visa, you may need to get the re-stamping upon the extension of your expired visa. Re stamping of H1B visa can be at any US consulate out side of USA.
Reference
http://www.h1base.com/visa/work/h1b%20visa%20stamping/ref/1466/