I am an Indian traveling to London for tourism. While in the UK, I am also planning to visit Scotland, so is its necessary to carry my passport with me or should I travel without passport?
There are no border/immigration checks between Scotland and England since, at the time of writing, they're part of the same country - United Kingdom. Hence you won't have to show your passport to immigration officers when entering Scotland from England and vice versa. You will nevertheless need to prove your ID to airline staff before boarding intra-UK flights, and your passport is perfect for this purpose.
That's not to say that you shouldn't carry your passport whilst travelling. IMHO it's always better to carry a valid form of identification at all times. In case of random ID checks you should always be able to prove your identity, although for this purpose a driving licence is sufficient in the UK. ID checks you can encounter whilst in the UK include those performed by bar/shop/supermarket staff to prove that you meet the legal age requirement to purchase or consume regulated products such as alcohol or cigarettes. Since you will probably be visiting tourist places note that you need to prove your age if you want to access youth or senior discounts (if applicable). Obviously for this you'll need some form of id. Having said this, note that you can of course leave your passport at home or at the hotel, should you be afraid to lose it.
As the answer by JoErNanO says, there are no passport checks within the United Kingdom. The border between England and Scotland is largely unmarked. Moreover, no one can require ID from you at random, the UK is not a police state.
If you are travelling by air within the United Kingdom (from London to Edinburgh for example) it is not legally necessary to bring any identification. However, your carrier may ask for ID for its own purposes, particularly if you are checking a bag, so you should check the airline's requirements. (On BA when asked I usually just show my BA Executive Club loyalty card!)
The main reason to bring any ID is to ensure you can get served at a pub.
If you are hiring a car you will also need to bring a driving licence.