On this clear early morning over London, I was studying the moon with a pair of binoculars and noticed a tiny dot of light that appeared to trace a slow orbit around the moon. I reckon it moved roughly 30 degrees in as many minutes. I'm wondering whether I was seeing a star or if it's remotely possible that I was seeing sunlight reflecting off an orbiting craft? Although the sky was clear it certainly wasn't starry; it was about 100 minutes before sunrise.
No. There are currently 5 spacecraft orbit the Moon (Or the E-M L2 point). These are LRO, Artemis P1 and P2, Chang'e 5 T1, and the Queqiao relay satellite. Of these, the largest is probably LRO. The solar panels, which are the largest part of most spacecraft, "he three panels together are 168 inches wide and extend out from the spacecraft 126 inches". Converted to meters, that is 4.25 x 3.2m. Just to give an idea of how visible that would be, Elon's Tesla Roadster, according to JPL Horizons, when it was at the distance of the Moon, had an apparent brightness of about 15.27. Using this chart, an aperture of about 50 cm is required. LRO should be a bit brighter, but not enough to make a huge difference. And none of this takes in to account the glare of the Moon itself. Whatever you saw, it probably wasn't a satellite.
I suspect it was a star of some kind. If you can provide the date and time we might be able to figure out a candidate star.
The other answer is conclusive (it probably wasn't a satellite). Let me just add more data w.r.t. time.
At the lowest altitude possible, a lunar orbit is completed in 1 hour 51 minutes. The higher the orbit, the longer it takes - say at 400 km altitude (similar to the ISS altitude around Earth), it would take 2 hours 20 minutes.
Let's say it takes 2 hours sharp. That's 120 minutes for 360 degrees, or 3 degrees per minute. In 30 minutes you would expect the satellite to do about 1/4 of its orbit. But it's pretty complicated to translate that into what you see with a telescope from Earth.
All of the above is for very low orbits, which in a small telescope would seem to graze the surface of the Moon. If there's any appreciable distance between the satellite and the Moon, the orbit would be much, much slower.