I have heard that US immigration will turn you away as a visitor if they believe you want to live in the US some day, even if you are going through proper channels and still retain ties to your current home. Let me see if I can find a reference. This forum is for folks who are waiting for "fiancé visas" and find visiting a difficult thing. It says:
The answer is yes, visits are allowed. But whether you will actually be admitted lies entirely in the hands of the officer questioning you upon entry. And face it, hearing you've got a sweetheart you're intending to/have married waiting for you in the US is going to set off a "he/she is just going to stay here forever" bell to that officer. It's your job to convince that officer that you have a life back in your home country that you fully intend, and will, go back to.
I suspect the situation will be very similar for you. Have paperwork with you about the job you hold in the UK and the car you own there and whatever else might make it clear you will be going back after this visit. There are no guarantees, any and all visitors can be turned away by an office having a grumpy day.
You might also have the opposite problem: once you're a citizen, you're only allowed to enter using your US passport. But you might not have the passport yet. That one I would take up with whatever consulate or embassy is processing your application.