You can use a donor advised fund in the UK to whom you can donate appreciated stock . As you note this allows you to avoid capital gains and provides a deduction. There is at least one donor advised fund in the UK which allows you to make the donation to both UK and US charities (National Philanthropic Trust NPT ). The Charities Aid Foundation in the UK is also long established - not sure if it allows donation to UK and US as well and seems to accept appreciated stock too. They have an extensive list of UK charities that have passed their scrutiny .
I have used NPT and they work well. However I think that I may have restricted my funds within the trust to the FTSE index which was probably not optimal! NPT are a bit more recent to the UK and do make the charity go through some hoops to make sure they are totally legitimate if they are not on their existing list . (this happened when I made a donation to my university). They charge fees which get significant if you hold less than about £15,000 in the fund . Certainly worth considering though.