There are some exaggerations for comic effect, but yes - there was an extensive amount of wealth leading to large incomes based mainly on rent and other investments, so that there was quite a lot of passive income flowing into the families. And many relatives would then receive an "allowance" that still left them quite well off so that they could afford fine clothes, club memberships, easy travel, and personal servants like a valet.

The wage structure and tax structure in the UK changed due to the world wars. There were still many wealthy families, but much less of a large support system with many family relations receiving an allowance, and so less of the "idle rich" that you see with Bertie Wooster and his crew.

But you can also see, in the same episode, the "working rich" shaking their head at Bertie not working. https://youtu.be/Te3SvM-aG04?t=1309