Go to Kensington Gardens and Hyde Park. On sunny days, they are the perfect spots to share lunch or dinner, or even go for a run.
Many supermarkets offer discounted sandwiches and cookies after 5pm every day, so stocking up for the next day's breakfast or lunch might only cut you back about 3-4 pounds, while ordering a full English would be about 9-10 pounds. Don't bother to buy water, since tap water is potable in England. Fruit is also great sustenance and curbs any hunger pangs when you are in high margin tourist areas. When you get the chance though, go ahead and try it. Personally, on a tight budget, it makes sense to cut back on expenses for two meals and splurge/experiment with one. That way, you could eat for a whole day for about 20-25 pounds, including one beer or a glass of Pimm's.
Regarding transport in and out of London across the country, book in advance to get the best fares. Rates on the day could be as much as double the prices booked even a day in advance. Trains are quick, but rather expensive. Buses are fairly cheap, but take a decent amount of time and might also involve a couple of hours stop at some godforsaken time in the night mid-journey.
London doesn't have to be expensive. You can easily get by on 40 pounds (or Rs 4000) a day including accommodation.