One of the pieces is about 4.5cm long (1.8in) and weighs just under 49g (1.7oz) while the second is 1.5cm long (0.6in) and weighs just about 14g (0.5oz).
The museum’s archaeology curator, Jon Marrow, said: “Though they may seem modest at first glance, these pieces offer an extraordinary glimpse into prehistoric craftsmanship.
“They are tangible traces of human activity from a time when gold held powerful social and symbolic meaning.”
The fragments are part of a growing body of evidence pointing to significant Bronze Age activity in the area.
Nearby finds include a copper-alloy axe head, a collection of gold fragments, and a bent gold bracelet, all within several hundred metres.
The museum is hoping to acquire the objects to put on display and for further research.
The grant funding has come from the Arts Council England/V&A Purchase Grant Fund.