To better constrain late Neogene denudation of the Himalayas, we analysed in situ 10Be concentrations in 17 Neogene sediment samples of the Surai section (central Nepal) and two modern sediment samples of the Rapti River. We first refined the depositional ages of the Surai section from 36 new paleomagnetic analyses, five 26Al/10Be burial ages, and, based on the Dynamic Time Warping algorithm, 104 automatically calculated likely magnetostratigraphic correlations. We also traced changing sediment sources using major element and Sr‐Nd isotopic data, finding at 4–3 Ma a switch from a large, trans‐Himalayan river to a river draining only the Lesser Himalaya and Siwalik piedmont, increasing the contribution of recycled sediments at that time. 10Be concentrations in Neogene sediments range from (1.00 ± 0.36) to (5.22 ± 0.98) × 103 at g–1 and decrease with stratigraphic age. Based on a flood plain transport model, our refined age model, and assuming a drainage change at 4–3 Ma, we reconstructed 10Be concentrations at the time of deposition. Assuming cosmogenic production rates similar to those of the modern basins, we calculated palaeodenudation rates of 0.9 ± 0.5 to 3.9 ± 2.7 mm a–1 from ca. 6 to 3 Ma in the palaeo‐Karnali basin and 0.6 ± 0.2 to 1.6 ± 0.8 mm a–1 since ca. 3 Ma in the palaeo‐Rapti basin. Given the uncertainties and similar modern values of ~2 mm a–1, the palaeo‐Karnali denudation rates may have been steady at ~1.7 ± 0.3 mm a–1 for the last ca. 6 Ma. A transient acceleration of the denudation in the palaeo‐Rapti basin of ~1.5 mm a–1 since ca. 1.5 Ma was likely due to the reworking of older, 10Be‐depleted Siwalik sediments in the foreland. If true, this steadiness of the denudation rates may suggest that Quaternary glaciations did not largely affect Himalayan denudation.