Upvote:1
This is really a "bug" in the construction of the J1: It is meant for people who leave their country of residence for some years to study/work at a university in the US and then return to that place. That's however not what typically happens, and in some places (like Germany) it is in fact not even legal to be a resident if you are not in the country.
In any case, the two options for the DS-160 are to either use your current UK address, or some address which works permanently, since e.g. your school might send you documents to that address. I don't believe it really matters for the application -- if you use your current address, you will get mailings before your stay more easily, but in that case you should communicate to your US school to not use this address to mail things to you after you return. (E.g., I did not receive a tax form after leaving since it was sent to my old address.)
Re-reading your question, I see that you are just doing an internship, which sounds like a shorter stay. So if you would be returning to the same address in the UK, I would definitely give that address.
What would be more tricky would be to list an address outside of the UK, since from a US perspective you are an academic visitor/intern from the UK (for instance, if you are paid you are also falling under the US-UK tax treaty, regardless of your nationality).