The best I can find in terms of an authoritative site for medicines in India is available on the World Health Organisation's India site, which has this list of Essential Drugs and Medicine in India - albeit from 2003.
However by far your best bet is to go to your local NHS doctor in the UK and ask them, as they'll have not only an up-to-date list, but also quite often when you travel the names of drugs change quite often. What's known as 'warfarin' in some countries is 'coumadin' in others (comes down to brand names and trade names and weird other issues).
As a result, you could end up going to a doctor in India and have him have no idea what you're talking about. (I've had this very problem).
Ideally your NHS doctor will know if the drugs you want are available - and more importantly, if they're not, what alternative is acceptable - he/she will know your condition and what you should take over there. If I'd listened to some of the medical advice in Tajikistan, I would likely not be around to type this.
As for whether you need a prescription, it'll be easier if you have one - either from a doctor there, or even better, initially, from a doctor in the UK - as some pharmacies will accept drug purchases without out (more likely outside Delhi), whereas others will insist on you having a prescription. Even if you take a photocopy of your normal prescription in the UK, this could go a long way (and prevent misunderstandings).
Some more information on that available on Thorn Tree.