You will need a tourist VISA for India. For UK Nationals this can be done online without the need to send your passport to the Indian Embassy.
World Challenge have produced a guide for completing your application which you can access here
. In particular it gives details of our hosts in Ladakh which are needed to complete the form.
(Make sure you apply for a Tourist VISA and not one of the other options. Don't mention volunteering, since this means something different to VISA authorities.
If required, please refer to the Community Engagement or Project Phase as 'Cultural Immersion' or 'Cultural Exchange'.)
Don't apply too early. Further details about applying are also on this site https://indianvisaonline.gov.in/evisa/tvoa.html
At time of writing the fee payable to the Indian Government for your VISA is $100 + 2.5% bank transaction charge