IELTS appears to insist that, eg, 'A number of people are going there' is correct form.

I should have thought that 'A' tells us that 'number' is singular. The plural, 'people' lies within the prepositional phrase 'of people' which merely limits the subject noun, 'number'.

Therefore it would appear that the verb should be in the third person singular, 'is'.

IELTS' rationale for their choice is said to be that they feel 'a number of' equals 'many' so 'are' is correct.

I came to the conclusion that, since they have such influence, one might agree that either was acceptable. I think 'are' is incorrect but I should be willing to accept it if its adherents were to accept 'is',also.

It is ten years now since I last taught for the IELTS exam & I still find myself toying with this connundrum.
I would value the opinions of others, preferably in non-abrasive terms It could be said that grammar does not matter until one reads the awful [miss]-usage in the British newspapers, etc, on-line but I still feel that one should always be light of heart, rather than aggressive about it.