A number of such incidents has/have been reported by the local
residents so far.
The number of such incidents is/are very low.
The number of elephants in Kerala has/have been dwindling.
You ask for British English. I'm British. However there are disagreements about this.
My opinion is that "number" is singular and so the verb should be as well.
"A number has been reported"
"The number is very low."
"The number has been dwindling."
It would seem very odd to me to say, "The number are low". However "The numbers are low" makes absolute sense.
Other people seem to be influenced by the plural noun following "of". Grammatically that is indefensible but lot of people say it that way so I suppose it can be considered acceptable.
Let's see what other opinions there are.