Accommodation
Luckily, I got the opportunity to live with family in London during the four months of my exchange which kept the living costs down for me. Generally, rent costs are expensive in London so be prepared for that. However, because my situation is rather rare for an exchange student I will mention a few alternatives for accommodation in the designated section!
Food
I spent a lot on food during my stay in London, on average £10 per day (ca 120 kr), sometimes less or more. Since I spent on average 8hrs in the lab from Monday-Friday I had to provide my own lunch. If you are looking for keeping the food costs down, bringing homemade food is cheaper which I did sometimes. London has a variety of groceries stores where you can shop at for breakfast, lunch and dinner. I bought groceries mostly at Tesco, Sainsbury's and Waitrose (the latter being more on the expensive side).
Imperial offers a great deal of food (hot meals, sandwiches, snacks, refreshments) at their cafés and restaurants and even better, as a student you often receive a discount if you have your student card. Every Tuesday during lunch time, Imperial hosts the Farmer's Market on the campus' Queen's Lawn which is literally a market with multiple food stalls offering hot meals from all around the world. The first time I bought food from the Farmer's market I tried a delicious Spanish seafood paella (enough to feed an entire family) for £6!
Transport
Since I did not live close to campus, I had to commute with the National Rail and tube to lab everyday. Therefore, the cheapest alternative for me was to apply for a 18+ Student Oyster photocard discount. If you are a student over the age of 18 and live at a London address during the term time you are eligible to apply for this photocard that gives 30% discount on adult tickets. Every month I would buy a monthly pass on my photocard which would cost me £131.40 instead of £188.20 for fare zones 1-4. The nearest tube stations to Imperial are South Kensington station or Gloucester Road which are both in fare zone 1. Please pay attention to the fare zone you live in before buying the monthly pass as this will change the price.
Student Union FeeI decided to get an Erasmus Membership, part of the Imperial College Union, for a one single payment of £5 on their website. This enables you to take part of activities organised for Erasmus students/union members at a much cheaper price. It is totally worth it!
Visa and Vaccinations
I was not required to apply for a visa or take any vaccinations (beyond the ones I had already taken in Sweden) before moving to London because I am from an EU country. However, this might be different for anyone who is not from the EU.