Discovery of the neutral currents:

Steinberger's Nobel lecture (Gargamelle's explaination in page 7)

Gargamelle detected two kinds of signal:
CC: ν_μ+N -> μ+hadrons
NC: ν_μ+N -> ν_μ+hadrons
The distinction was that in the second case there was no muon in the final state. This led to a background from neutron interactions, with neutrons coming from the beam.

(Less abundant, but observed, where also the CC and NC events from collisions of neutrinos on atomic electrons. The outgoing electron is ejected at small angle wrt the beam direction, θ_e~√m_e/E_ν.)

From here:

Since the neutrino cross-sections on nucleons were more than two orders of magnitude bigger than those on electrons, a clear understanding of the background, rather than of statistics, was the main problem. The first step for the Gargamelle collaboration was to resolve to look for inclusive events of the type ν + N -> ν + hadrons, rather than exclusive processes, which would be more difficult to identify, and to select only the highest-energy events, with total hadronic energy E > 1 GeV.
Events with identified hadrons only were called "NC", for neutral-current candidates, as compared with charged-current ("CC") events containing a charged lepton (muon). "AS" events were those in which a CC event had an associated "star" due to a secondary neutron in the same picture (figure 1).
Suppose that a number B of the NC events are due to neutrons, then if we take a simple one-dimensional model with all particles travelling along the beam and chamber axis, the expected value of B can be easily calculated from the number of AS events (...) This attenuation length was calculated from the shape of the neutron energy spectrum measured in AS events and reasonable assumptions on the elasticity of neutron interactions.
(...)
Clearly the B:AS ratio simply states that for L (lenght of the chamber) << λ (interaction lenght of neutrons), the neutrons entering the front of the chamber are generated by neutrino interactions from an upstream region in the shield (...), while inside the chamber the AS neutron stars can be generated by neutrino interactions anywhere inside a distance L, less an amount λ for neutron detection. By using this equation, one calculated B/AS = 0.7, compared with the observed ratio of NC/AS ~ 6.0. This implied that only about 10% of the NC events were due to neutrons.
(...)
It happens that the simple one-dimensional approximation works because of the relatively high energy of the hadronic events, so that most of the neutrons do enter the front face of the chamber.
Confirmation that the NC events were produced by neutrinos came from measurement of the longitudinal and radial dependence of the NC:CC event ratio in the chamber, which was found to be constant within the statistical errors, whereas a predominantly neutron origin would have shown strong dependence on longitudinal and/or radial distance.