You can carry more than 10 000 US$ on your person, but just need to declare it to customs of the country you are leaving and/or entering.
So this would apply to India and the US, UK is just a transit point, and since you are not entering the country you will be fine:
http://www.hmrc.gov.uk/customs/arriv...aring-cash.htm
For the US: Note that the 10000 limit applies to assets with you, not just cash, so fill out the US form and have it handy to submit:
http://www.fincen.gov/forms/files/fin105_cmir.pdf
This form is meant to stop money laundering practices so reporting what you have with you will not lead to questioning, but may be reported to the IRS.
For India: other than visitors, you are not allowed to export foreign currency unless you bought the currency through legal channels. See page 14 on this guide:
http://www.cbec.gov.in/Guide.pdf