This is now part of the grounds of Round Hill caravan / camping site, but you can certainly walk straight into the site from Hatchet Moor / Beaulieu Heath.
The barrow is now fenced in, presumably to stop kids and mountain bikes damaging it. It certainly looks a bit worse for wear, but the fence should now protect it, and it’s nice to see a good English Heritage / Forestry Commission info board on the East side which should help educate a few bored campers. A brief conversation with a charming extended family of campers who had been having a piss-up on the airfield suggested that it had only recently been fenced in. The board says that most of the Beaulieu Heath barrows were destroyed in 1941 when they built the airfield. This one is now a Scheduled Ancient Monument. It’s a similar size to the other barrows I saw in the New Forest (about 20-25m diameter, 1 to 1.5m tall)