Yes, Indian students can ask to settle in the UK after they finish studying there. The rules change based on the visa type (Tier 4, Tier 2, etc.) the student uses. Usually, students need to work in the UK for at least five years to qualify for PR.
There are ways to spend less on studying in the UK. First, find scholarships and grants for international students. Look for student discounts from businesses. Lastly, shop around for cheaper accommodation.
Many choose business, engineering, computer science, and humanities. The UK also has good programs in law, economics, and social sciences. Make sure to ask the institutes for the latest info and to clear up any questions you have.