In summary, depending upon the type of crossing in question, the barriers will either (in the case of 'full' barriers) be controlled by a Signalman - remotely with CCTV supervision or locally from an adjacent signalbox - or (in the case of 'half' barriers) be automatic - monitored remotely by the supervising signalbox or locally by the Driver of the approaching train.
I suspect, without checking and without much local knowledge, that the crossing in question is full barrier CCTV? In that case, the operation of the crossing is very much in the hands of the supervising Signalman who must at least confirm that the crossing is clear (by CCTV) before the protecting signals can clear - the barriers themselves
may be able to be set to lower automatically though.
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Beaten to it!
I'm not sure about more traditional gate crossings with people to close the gates themselves, I assume the signaller gives them an indication of when they need to close the barrier.
Often the crossing will be operated by the Signalman, either by hand or by wheel (or, in a few cases, with power assistance!). In other cases, where the crossing isn't adjacent to a signalbox, a Crossing Keeper will close the gates and clear either his own signals or a slot on someone else's signals - there's various means of informing him when to do this.