I am really sorry to be negative, but this mound does not feel like a tumulus to me. It is more rectangular than round, and this part of the park was used as an US Air force base for a while from 1944. In fact the D-Day landings were planned from here by Eisenhower.
The ground around is littered with smaller raised areas. Perhaps where corrugated iron huts once stood.
I haven’t looked this up on any national monuments record and the OS Explorer map 161 shows nothing, but its provenance seems secure as it is mentioned on the Royal Parks website and by local walker/historian/writer David McDowall.
The Royal Parks website says that “The flat site of Bushy Park has been settled for at least 4,000 years. A Bronze Age barrow & burial mound was excavated near Sandy Lane and the contents are now housed in the British Museum.”
It also adds that the park contains “clear remains of mediaeval settlements, with the finest example found South of Waterhouse Woodland Gardens, where there are traces of the largest and most complex mediaeval field system in Middlesex.”
To find the barrow walk into Bushy Park by the Teddington Gate, turn left and walk along the path for about 250 metres. This is it – only a small hump, and now of an irregular shape, but it is a barrow, unbeknown to all the walkers and cyclists who go straight over its top. David McDowall says that it originally ran beyond the park wall.
‘Prehistoric London’ by Nick Merriman (1990 – ISBN 0112904475) says that “the only definite prehistoric burial mound (or ‘barrow’) in the London area used to be in Teddington, and was excavated by a group of antiquarians in 1854. It was originally nearly 30m across and 4 m high, and contained at least one central burial (probably a cremation) which yielded a bronze dagger and flints, and various other burials inserted into the mound as later date. Unfortunately, only a few flints survive from this poorly-recorded excavation.”
There is a 'Bushy Park History Room' so if anyone wants to research the barrow maybe they could try here. It is staffed by volunteers, and located within White Lodge at the Stockyard. Visitors are welcome by prior appointment with the Park Office, White Lodge, The Stockyard
Bushy Park, Hampton Court Road, Hampton, TW12 2EJ. Tel: 020 8979 1586. Fax: 020 8941 8196. This info was taken from www.royalparks.gov.uk/bushy_events.htm