Besides London Walks which I’ve done and enjoyed might I offer the following for a solo sojourn.
I’m in London every year and love early morning solitude.
If you are near Lancaster Gate walk into Hyde Park through the gate by the Italian Gardens. Gardens were a gift from Albert to Victoria. Head for the Princess Diana Memorial Fountain. Paths are well signed. Your paved path with be adjacent to the Serpentine. You’ll see a number of runners, dog owners, swans, geese, ducks and possibly lovely green parrots. You’ll also see the strange Henry Moore sculpture and the intriguing Isis statue. Passing the Diana Memorial fountain ( opens at 10am maybe earlier) you will come upon the Lido Cafe which opens at 8am. You will also see swimmers doing laps. Nicest place to enjoy a morning coffee sitting outside watching Londoners begin their days. From here you can make you way to see the Albert Memorial and across the road Royal Albert Hall. Then into Kensington Gardens and over to the Round Pond ( more waterfowl) and then to Kensington Palace. Lovely walk
Just an idea for a walk you can do on your own.