You're right, I wrote that incorrectly, sorry. I've actually been paying UK taxes on the arising basis for some time, but remittance was a concern when I first moved here (with no UK income but weird US income situation). I didn't end up paying on remittance basis but it stumped a couple of tax advisers, so I think worrying about moving money from the US to UK stuck with me.
The question still stands: are there ever any concerns (tax or otherwise, aside from the usual caveats about reporting >$10K) about moving money in the OTHER direction, UK income to USA? My understanding is that since the US taxes on worldwide income, it should not be an issue and I'm fine to move it over.