As you might be aware, living in London is very expensive! Nevertheless, so is living in Stockholm. London is more expensive overall because accommodation is more expensive. On the other hand, buying food in stores is pretty much the same price as in Sweden and usually eating out is a bit cheaper than in Stockholm.
For example, for a single room en suite (with my own bathroom) and a shared kitchen in the Imperial student hall, I payed £210 per week! It is very expensive but worth noting that the shared kitchen was cleaned every day and my room + bathroom once a week. There are nevertheless some cheaper options. For example, you can rent a "standard twin" room where you can share a room with someone else and the bathroom + kitchen are shared with a group of people (in that case the rend is around £115 per week).
Additionally, transports in London are almost double the price of transports in Stockholm and therefore quite a lot of money goes into that (depending how far away from the university you live). I highly suggest that, once you have been accepted by Imperial college, apply for a student oyster card as it will enable you to get the student discount:
https://tfl.gov.uk/fares-and-payments/adult-discounts-and-concessions/18-student#on-this-page-0
Finally, when going to Imperial, there are no obligatory costs as the student union is free and no visa nor vaccinations are needed.