I wouldn't say many because, in this case, we are only talking about the landed aristocracy. By the turn of the 20th century, the hereditary peerage was given out more liberally as a reward to people who were previously noble. There were a lot more of them than the traditional "estate lord." so there would not have been a huge number of nobles going bankrupt, however, many of the landed nobles were. The bankruptcy had less to do with failure to modernize as much as taxes. By WWII nobles were paying enormous rates on income and inheritance. The Death Duty, for example, was an inheritance which increased over the years to the point where estate owners were paying 50-60% in taxes on it. Given the fact that their income was based solely on the land (which by nature, is not scalable and following the agricultural depression in the 1870s, almost unviable), these taxes were difficult to pay. The houses on these estates were also becoming a problem. The houses that we think of when we think of a British estate were relatively new as the country lifestyle had changed so to did the houses to accompany it. These places required an army of staff to keep it running. After WWI, the people just weren't there, and many were leaving for better wages elsewhere. This increased the expense of upkeep. Ultimately, nobles families decided to dismantle their homes in the country. Some were able to keep their London houses, but usually, these were the first bits of property to be sold off to cover the cost of the country estate. No noble family really makes an income on their property (the land) today if they were able to keep it. The forward thinkers married money, started working (the aristocracy never worked), or commoditized their homes like the Downtown Abbey house.