Visitor Visa extension (US citizen)

[Kirodoc]

I'm unclear on whether this is the proper place for this, as all of these visa types are a little confusing. My family (wife and 2 young children) and I are touring Europe for the next few years. We have fallen in love with England and aren't quite ready to leave. We entered the UK without applying for any visas, as US citizens get 6 months in any 12 month period. We have left once since arriving, going to France for 18 days. Our 6 months is almost up and we'd like more time. Is there any possibility of this being allowed? I've seen mention of temporary leave extensions and other extensions, but was unclear as to whether we fit the criteria.

I'll note that we have adequate income (over $100K USD yearly), a US and a UK bank account and several character references, both personal and professional. We also own a car and caravan, both purchased in the UK. We have no marks on our records either in the US or UK such as criminal records or some such. I have a Doctorate and my wife has a Masters degree.

Any insight is much appreciated.

[Wanderer]

Not possible in these circumstances.