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There is a walk-in clinic near the Moorgate Tube Stop at which you can arrange a 15 minute consultation for GBP 55.
You can book an appointment via their site, or by telephone. The clinic at Moorgate is given here as an indicative sample only, there are other walk-in clinics in central London that may be more convenient. I have never attended that particular clinic (and have no connection to it), but have used the walk-in clinics both at Kings Cross and Marylebone.
You will need to pay and then reclaim the expense from your insurer in the US.