Tenants in Ealing were the fifth highest in England at risk of losing their home in the last year, according to the homeless charity Shelter.
Shelter says this is down to a shortage of affordable homes combined with government welfare cuts.
According to the charity, one in 28 households in Ealing were at risk last year, with one in 29 in Hillingdon and Brent and one in 30 being at risk in Harrow.
Those figures are way above the national average for the whole of England, which stands at one in 50 renting households.
A total of 2,165 rented households in Ealing, 2,243 in Brent, 1,324 in Hillingdon and 993 in Harrow were all under threat of eviction in the past year, according to the figures.
Additionally, the volume of people facing eviction who are coming to Shelter for advice is getting higher and higher.
In the past year alone, more than 9,800 people facing eviction have called the Shelter helpline for advice and 500,000 people have visited the Shelter website's eviction advice pages.
Nadeem Khan, helpline adviser for Shelter, said: "Every day at Shelter we hear from people who are struggling to keep up with their rent, many in total desperation after the court papers land on their doormat and the threat of being evicted becomes very real.
"It's natural to feel overwhelmed, but remember you're not alone – Shelter is here 365 days a year.
"If you're struggling to keep up, or facing eviction and not sure what to do next, get expert advice as soon as possible. It can be the difference between losing your home and keeping it."
However, house prices in parts of west London are rising at more than £150 a day according to figures from the new official house price index.