Tucked between Charing Cross Hospital and Barons' Court tube station is Margravine Cemetery, once known as Hammersmith Cemetery. It's a long corridor of a thoroughfare, either side of the busy path lined with graves. Like most suburban cemeteries, it's not over-supplied with spectacular monuments, though Margravine has a decent crop of quirkiness: check out the Fletcher family's throne, and bandmaster Tom Brown's cello, now sadly damaged. Spectacular in both name and monument is Sextus Gisbert van Os: pillows on graves are not that unusual, especially in west London, but his is one of the best examples I've seen.
The cemetery is being nicely managed as a mix of Victorian burial ground and wildlife habitat by the London Borough of Hammersmith & Fulham, with help from the Friends of Margravine Cemetery. There are no new burial spaces available in Margravine, though interments can still happen in family graves.
"Margravine", by the way, is the female form of "margrave"; the cemetery is so named now because it's on Margravine Road. The margravine in question is Elizabeth Craven, the Margravine of Brandenburg-Ansbach (who looks like a rather interesting person). The Margravine herself is buried in the English Cemetery at Naples, also the resting place of Mary Somerville.
Visiting: Public transport to Hammersmith station, it's a 5 minute walk. From Fulham Palace Road, turn down St Dunstan's Road, on the north side of Charing Cross Hospital, and right into Margravine Road. Cemetery has a lot of livings in it, mostly passing through. No one acts like photography is weird.