Basically, there's no set period, but if it looks like you are trying to use the visitor visa to live in the UK without a proper visa, you could be refused entry.
So, they are on the look out for:
- someone who has spent a lot of time in the UK on many visits
- someone who spends more time in the UK than in their home country
- someone who does not seem to have ties in their home country to return to (job, home, family etc.)
The general rule of thumb is to spend at least as much time outside the UK than you spent inside... so if you visit for 3 weeks, go back to the US for 3 weeks or more. If you visit for 5 months, stay away for 5 months or more before coming back.
Also, the shorter your visit each time, the better... because it's more common for people to only be able to take a short vacation to the UK, rather than a trip of several months... the longer you try to stay in one go, the more suspicious it will look.
So, when you come as a visitor, you need to be able to show:
- a return ticket within 6 months
- enough money to support your trip without working
- evidence of a job to return to (letter from employer stating you have been given time off and what date you are coming back to work)
- evidence of a home to return to (valid rental agreement or mortgage statement)
- evidence of any other ties to the US that you must return for (family to take care of, appointments, interviews or other commitments, things like other trips or weddings or parties etc. you will attend - things like that)
It's also good to show you know the visa rules - that you can't work as a visitor (in any capacity, even online, remotely or unpaid), you can't stay more than 6 months and that you must return to the US to apply for a fiancé or spousal visa.
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