[chongli]

In other words, calling a multi-million pound property a “cottage” would rankle an American ear.

I don't think so. There's tons of multi-million-dollar lakefront properties all over North America. People generally refer to these as cottages since they're:

1. seasonal

2. not the primary residence

3. often located near a body of water and/or away from big cities

4. intended for vacations with families and friends (or short-term rental for the same purpose)

[mannykannot]

Indeed... This usage reaches across the pond - check out how the Vanderbilts used the term here:

https://www.architecturaldigest.com/story/guide-to-vanderbil...

Le Carré's cottage is a splendid place, but it's not the Breakers.