If you are an international or visiting student there is a great resource on Western Univiersity's website.
This site provides info on the different types of housing available. On-campus residence is not likely to be a viable option unless you plan on arriving/leaving at scheduled start/end of semester times. The Platt’s Lane estates and University apartments are good options if you want to be close to campus but they usually have wait time that may not work for your arrival. Good to look into availability. The “off-campus housing” section has a lot of useful information about the different neighborhoods in the city of London and things to look for and to ask when securing a place to live. They also have contacts listed who can help set you up with housing contacts if communication is an issue.
I have some details about off-campus housing locations from my own perspective written below. There are a lot of apartments available year-round and a lot of options for shared housing and renting furnished rooms. You can search Kijiji and Facebook Marketplace to find a lot of options. There are also Roommate Wanted groups on Facebook where you can look for housing and post details about the type of housing you’re looking for. There are also a lot of options on the University’s off-campus housing website.
Regarding apartment hunting, if you are eager to stay near the university there are a variety of areas you can focus on. Two of our lab members, Patrick and Janice live at Windermere Place. It is very close to Western University but you would need to take a bus/Uber/cab for groceries unless you have a car. But it's on a very nice street in a good neighbourhood, mostly university students and employees.
There are also a variety of apartment buildings on Adelaide near Kipps Lane (I've included a google map shot of the places). These apartments will be in a less ideal/more sketchy neighbourhood but are very close to amenities (within a block of shoppers drug mart, restaurants, inexpensive groceries etc). There will be a lot of students and lower income families in this area. It's a very convenient location and will likely be less expensive.
There are also a lot of apartments buildings in the Platts Lane/Cherryhill area (I've included a google map shot of the places). This a good location right beside a mall with amenities including a grocery store and shopper's drug mart. It has a high proportion of seniors in the area mixed with university employees and students.
Of course, the closest apartments will be those on Richmond St. (I've included a google map shot of the places) You'll be very close to the university but will need to take a bus/Uber/taxi to get groceries and there aren't many nearby amenities.
There are also a variety of places in the area on Wonderland Road between Sarnia Road and Oxford St. There are a ton of shops, restaurants and businesses in this area so it very convenient but also very busy. There are also a lot of new build townhouses and such in the area if you wanted to try and find a nice rental with a yard, but they'll likely be quite pricey. Most of the apartment buildings I've listed will be very basic, run of the mill layouts and finishings for the best price. To find a more private or more unique rental you'll have to do some digging on Kijiji, Facebook Marketplace or you can look on Western's off-campus housing site.