Length of Stay in Europe w/o a Visa
 

I live in the U.S. and work independently as a writer and will continue to do so as I travel, therefore I will obviously not be looking to find work overseas. That being said, what is the maximum length of stay I'm allowed in the UK without a Visa? I'm stay in either London or Scotland.
Thanks so much for the help!

Do you have a US passport?
If so, and depending on what the Border Force agent decides upon your arrival, you can stay for up to six months in the UK without a visa. I am not sure you are actually allowed to work during that time.
You will need health care insurance to cover your entire stay. The NHS will charge you for any treatment you may need under their new strict rules.
The agent may decide not to give you the full six months if they are not convinced you are planning to leave again.

In most of Europe you are limited to any 90 days within 180. It is complicated to work out but thhere are online calculators to help. Again you will need health care insurance, and you are not allowed to work in Schengen on a visitors visa waiver.

6 months in the UK, but you are not allowed to work, even remotely by computer, even to volunteer. For that you need a temporary work permit. All of this information is readily available online.

The operative words are 'UP TO' 6 months. That is the max a US passport holder is allowed in the UK. But it is up to the border agent (immigration officer) to grant that long or not. If it appears you intend to work while there you could even be turned around and sent home on the next flight.

If you tell them how long you intend to stay (they do ask) - then you will be asked a lot more questions like how you will support yourself, what connections you have back home to show the likelihood that you'll return and not over stay, whether you have insurance or means to pay for medical care, how much actual money you have etc etc etc.