Work From Home for American Company while splitting time in Chicago andin London

Currently I'm touring around Europe while I work from home for an American company.  In the past month I met a nice girl that I'd like to get to know better.  My thinking is that since I work from home and my company is ok with me traveling and working. That I can spend 3 to 5 months at a time in London getting to know her and then go back to USA for about a month and then return to London for 3 to 5 months again.  I've been doing this for about 7 months and I've also been traveling around Europe every 4 to 6 weeks.  While I've been doing this every time I go through Immigration to go back to London where I'm staying immigration keeps asking how long I'll be in London and review documents of my return flight and my bank account to confirm that I will not be using public funds or working illegally.  In September, I'm planning on returning back to the USA for a month or so because my lease is up so I plan on closing out my lease moving my things in with my friend and plan to continue splitting my time between living in Chicago (1 Month) and London (3 to 5 Months)   at a time.  Is there any possibility that they will deny me entry as I tell them I'm simply a visitor?  And is there something I can do so that I do not have to worry about getting denied entry? Or if there is something else I should be aware of I would love to know. 

Thanks

Have you mentioned your working situation to the immigration officers? Because you're not supposed to do any work at all on a visitor visa, even for a US company.
If you have been telling immigration that you're just visiting and then working remotely, you have actually been breaching the terms of your visitor stamp and using deception to enter the country. They take a very dim view of this and it could result in a 10 year ban from entering the UK. Visitor visas are for visiting, not for living. If you want to live here you need to get a visa that allows you to do so.

While I've been doing this every time I go through Immigration to go back to London where I'm staying immigration keeps asking how long I'll be in London and review documents of my return flight and my bank account to confirm that I will not be using public funds or working illegally.

Um, actually right now, what you are doing is working illegally in the UK.

You cannot work in any capacity while you are visiting in the UK - this includes:
- working for a UK company
- working for a US company
- working for yourself
- working online
- unpaid work
- paid or unpaid volunteering

If you are here on a visitor visa, it is illegal for you to work for your US company in any capacity.

Is there any possibility that they will deny me entry as I tell them I'm simply a visitor?  And is there something I can do so that I do not have to worry about getting denied entry?

First off, you can stop working. Completely.

If immigration find out you have been working, or that you intend to work on future visits, and that you have told them you are not working when you actually are, they can determine you are using deception to enter, which can lead to a 10-year ban from the UK.

Also, while there is no hard and fast rule about how long you can be in the UK as a visitor, if it looks like you are using the visitor visa to essentially live in the UK (which it sounds like you are), they can refuse you entry to the UK at any time.

The general rule of thumb to try to stick to would be to spend at least as much time outside the UK as you have just spent inside the UK before you try to come back... so if you spend 5 months here, you should spent at least 5 months back in the US before trying to return to the UK.

Thanks for the insights, well is there a visa that I can get that would allow me to stay but not take any public funds?

Thanks for the insights, well is there a visa that I can get that would allow me to stay but not take any public funds?

It's not really about public funds, they don't want people living in the UK without either studying, working a job that no one else in the UK can do, or being married to a UK citizen. The fact that you won't claim benefits isn't in itself enough to qualify you for a visa. You wouldn't be entitled to benefits anyway, even if you wanted to claim them .

There's no visa that would allow you to live in the UK without studying, working, or marriage. To get a Tier 2 visa for working here, you would need a job with a company that's able to sponsor visas and fill a post that can't be filled by anyone else in the UK or (for the moment) the EU. If your relationship progresses to the point where you're ready for marriage you can get a fiance or spouse visa. You can go back into full time education. Those are your options. The "let's shack up" visa, as it's known on UKY, does not exist.

Would your company sponsor a work visa for you?