Europe Extended Stay

I don't know about the UK end of things, visa or otherwise; with luck an informed UK resident will clarify that.

As for the Schengen Zone, you need to be really careful about dates, because both your arrival date and your departure date count. If the UK has a similar 90-day limit (I haven't researched that) and has the same policy, you've got a problem, because the day you move from Germany to England (as an example) counts as a day in both countries, which means you can't just switch back and forth every 90 days. Now, if you were lucky enough to arrange your international transportation so you left area A before midnight and arrived in area B after midnight... But that requires a precision I wouldn't count on from planes, trains and ferries, and you'd have to be sure that the inbound immigration procedure/stamping of passport occurs at the end of the flight/trip, not at the departure point.

In general, my advice is to remember Murphy's Law. I've had 2 of 5 Channel ferries canceled on me, and one those cancellations occurred after the advent of the Schengen Zone. I was lucky that the missing ferry didn't result in a Schengen violation. I also managed to get sick on about Day 84 and remain sick until Day 89; that was a close call.

If there is a 90-day limit in the UK, I suspect what you need to do is not plan to use the UK as your only escape point, so you can plan Schengen time of only 88 or 89 days per cycle, to be a bit safer. Look into other options for spending time outside the Schengen Zone. Although this is subject to change, at the moment you can run for Croatia, Montenegro, Serbia, Macedonia, Albania, Bulgaria, Romania, Turkey, Ukraine, Russia. I assume also Ireland, unless there's some sort of cooperative agreement with the UK.

The UK does not have a 90 day limit, it is 180 day. There is no Visa for US citizens.

Are you a USA citizen? The U.K. may grant you access for a period of six months but it’s not automatic. A US tourist entering the U.K. for the first time may or may not be quizzed about their onward plans. You may well be asked detailed questions about your finances, and repeated entries every three months may be picked up as attempting to game the system or achieve immigration by stealth. You may or may not be allowed in, or may find you’re given a shorter time there.

The limit for the Schengen Area is "90 days in any 180". The Schengen Area includes France an Germany (and many others), it is the same 90 total for both, NOT 90 days in each.
"Any 180" means a rolling limit. Or put another way, every morning when you wake up you ask yourself "how many days, in the last 180 including today, have I been in the Schengen Area?". If the answer is less than 90, you can stay (or re-enter). If it is 90 you must leave that day. If it is over 90 you have broken the law.

If you spend 90 days in the Schengen Area (Germany or elsewhere) and leave on day 90. That day is also day 1 for the UK. Move forward to day 181, you now have only 89 days in the last 180 in the Schengen Area, so you can re-enter. But this is day 92 in the UK.

• The limit in the UK is 180 days, but, if they see you repeatedly coming back, they may refuse entry.
• Going up to day 90 is risky, if you have any delays you could go over the limit.
• Make sure you know where the stamps are in your passport, in case the immigration officer doesn't spot one and wrongly thinks you have gone over.

That "rolling date" thing makes my head swim, especially if you make multiple entries in and out of the Schengen zone. But with one-90-day stay, it seems to mean that you cannot just come back after 90 days in the U.K., because they will look backward for the 180 day limit period as well as foreword. See here:

http://www.schengen-calculator.com

So continuing with Chris' example, you leave Germany on Day 90 and enter the U.K. that same day. You stay 91 days there "just to be safe" and then travel to France, expecting to stay another 90 days in a "new" 180-day period. But if they look back for the 180-day period, on Day 181 you will already have spent 89 days in Schengen. So you get me day, not 90.

Do I have that right?

Sasha, it is actually simple, it just sounds complicated. You wrote:

because they will look backward for the 180 day limit period as well as foreword

No, they never look forward, only ever back.

you leave Germany on Day 90 and enter the U.K. that same day. You stay 91 days there "just to be safe" and then travel to France, expecting to stay another 90 days in a "new" 180-day period. But if they look back for the 180-day period, on Day 181 you will already have spent 89 days in Schengen. So you get me day, not 90.

Day 90 for Germany is also day 1 in the UK. If you stay 91 days in the UK, that only takes you up to day 180, so you can't go back yet. You need to stay 92 days: UK day 92 = Schengen day 181. You now have 89 days in the last 180 and you now have 1 day free. And on day 182 you have lost one day of the front, and gained 1 day at the end (88 + 1), so you are still OK, etc. etc.

expecting to stay another 90 days in a "new" 180-day period

There is never a "new" 180 period, it is rolling, and you never get another 90 days as one big chunk, individual days fall off the end one by one.

But I would never advice making it that close. The immigration officer may question you if you try to enter with 89 days in the last 180.

You may get extra scrutiny from both the Brits and Schengen zone officials, but in general your plan is workable. How many times are you thinking of doing the back and forth? Try it too many times and someone might consider you a resident or not really there for short term tourism and deny you entry.

Entering the UK or Schengen three or four times a year is nothing. Non-Rick Steves travelers, those who travel for a living or for business, may enter twice as many times as that. I've done it. The UK even has a program for people who enter often called "Registered Traveler." It allow those enrolled to bypass talking to anyone and use the machines like UK citizens. (I have it.)

Going and coming every 90 days is not excessive entry. However, what they will be concerned about is what you plan to do and how you plan to pay for your visit. If you can't prove that you have enough funds to take care of yourself without working, they may refuse you entry. They've also asked my itinerary. The UK seems to do more questioning than most of Schengen.

And I agree, don't wait the entire 90 days in Schengen. Give yourself at least a 2-3 buffer zone.

You don't "keep your visa going." There is no visa. When you arrive, you are given entry up to 90 days in Schengen and 180 days in the UK. As long as you don't go ove their stay rules (90 in 180 for Schengen or 180 days in the UK) you won't have stay problems.

I do not believe that multiple entries into Schengen will be a problem at all, but multiple entries for a long (89-day) stay each time, combined with similar periods in the UK, could raise a presumption that you are working there surreptitiously. They may question you closely regarding your means of support.

Or maybe it is OK to be self-employed and work there on one’s computer, earning money from US clients which goes into ones bank account in the US?

Or maybe it is OK to be self-employed and work there on one’s computer, earning money from US clients which goes into ones bank account in the US?

No it isn't, that would still count as "working". It would require a work permit. You would be a resident and liable to income tax.
Working on one's computer requires a good, reliable internet connection. Hotel internet is rarely that good.

The normal rule applied is whatever country you spend the most time in in a financial year, is your residence and where you pay tax. The "90 days in 180" limit keeps you under 6 months in the Schengen Area, and the UK 180 days limit also keeps you under 6 months. As you approach these limits, you could have problems. For example 5 months of a year in the UK, 5 months in France and 2 in the USA could make you liable to tax in the UK or France.

You also need to consider medical insurance for this extended stay.

All of your input has been helpful. I will be retired and not working. I am a US citizen. It sounds like my best bet is to start in the Schengen zone first for something less than 90 days. Then spend something less than 180 days in the U.K. Then I can go back to the Schengen zone for something less than 90 days. I will bring proof of finances and ihealth nsurance . Can you think of anything I have missed?

Make sure whatever insurance you have will conver you where you are going and I also sugest taking out a supplemental medical evacuation policy. You can buy them as annual policies.