How do you invest your money

If I elect the arising basis instead of the remittance basis, don't I lose the ability to avoid paying UK taxes on non-UK workday income?

Yes you do. So if you have a lot of non-UK workday income, you might be best using the remittance basis. You just need to do the math for both scenarios to figure out which is best in your situation. Good luck!

Yes, you can use the remittance basis to shield your US capital gains from UK taxation. Just keep in mind that once you hit the £2,000 threshold for total unremitted offshore income during the UK tax year (including dividends, capital gains, wages, whatever), you lose your personal allowance. In that case you may be better off using the arising basis, keeping your personal allowance, reporting the US mutual fund income to the UK and taking a foreign tax credit on your UK return for any tax paid to the US.

Assuming I make over £100k, I lose my personal allowance anyway (http://www.hmrc.gov.uk/rates/it.htm).  Under that scenerio, exceeding the £2,000 threshold would have no effect, right?  So until I've been resident 7 of 9 years, is it accurate to say that I don't really have to worry about my non-UK investments?  (Except to the extent that if I want to remit them to the UK in the future, in which case any pre-assignment capital will not be taxable upon remittance, but any interest/gains on such pre-assigment capital will be taxable upon remittance.)

Perhaps I am mis-reading something, but if you are taxed on the remittance basis, aren't your US capital gains taxed as offshore income and only taxed in the UK if you remit?

I am planning to move next month from US to UK for several (under 3) years and plan to keep US mutual funds in a taxable account.  I will leave any dividends and cap gains from those funds in the US.  If I'm missing something here, please let me know.

I am a UK/US dual citizen and if I move back to the UK with the intention of staying permanently I will probably have to pay UK tax on my worldwide income. So any capital gains on US based after tax mutual funds will be taxed as income. However, I should be in a fairly low tax bracket as my plan is to minimize my need for income by buying a house with cash so I don't need a mortgage or to pay rent.