grammatical-numberpremodifiersthere-isverb-agreement
I believe it well established that the choice of whether to use "There is" or "There are" with the phrase "a lot of" depends on the following word. For example, you would say:
What is the right form to use for a pair of, a bunch of, a group of, etc.?
This is a very good question. I think the difference is between a comma-separated list of three or more subjects, and a simple ("and"-separated) two-part compound subject.
Let's take the slightly longer list: "When I opened the fridge there was only a bottle of milk, some eggs, a loaf of bread, and butter." In such a list, the items form clauses in the sentence; each one could be the singular subject or object of the exact same sentence: "... there was only a bottle of milk", "...there was only a loaf of bread", etc. You could also remove either of the two inner items with no change to the rest of the sentence (the fact that I was able to add the extra item to your quoted sentence without changing anything else in that sentence demonstrates this). In this case, the first rule you stated is correct; you pick the verb conjugation that works for the first item in the list, as if it were the only one.
However, when you get down to two items, now there are no more commas. The two items, say "a bottle of milk and butter", now form a compound subject; the two items are being referred to as one entity, which is always plural. In this case, the plural verb should be used.
EDIT: Good points. Some of those sentences sound better than others:
There is further rain and strong winds forecast for the next three days. - Not bad. I think "are" works here too.
There was a loud bang and some flashes of light before flames started pouring from the windows of the house. - This does indeed work better with "was" than "were", no question
There is a bank and cash machines in the city centre. - this one grates my ears; "there are a bank and cash machines" sounds much better for some reason.
There was no water or animals anywhere in the desert. - OK, but I think "were" sounds better here as well.
The biggest question, given the above, is why there is a difference between the second and third sentences; their structure is practically identical, the only difference I can detect is tense.
This question is more complex than it may appear. There seems to be consensus that a singular verb should be used in formal writing whenever the subject of a sentence is more than one [noun], or at least that this is (much) better than ?there are more than one. I subscribe to this.
It does not matter how many things the writer might expect there to be in reality: it is always if there is more than one species.
Nor does it matter what noun comes after one. It is always is; the word one forces a singular verb without apparent exception.
But why does this at all surprise us?
We are puzzled by this construction because the subject does not agree with the verb—at least not if analyzed according to conventional grammar. Consider the following sentence:
There are more men in the room.
Is would be impossible. The sentence is easy enough to analyse:
No problem there: subject and verb agree. More men is the subject, or at least the head of the subject.
There are more men than just John in the room.
The core of the syntax remains the same; the core of the subject is still more men. The addition than x is either an elliptical clause or a prepositional phrase that is part of the subject, depending on your model; in any case, than x is not what determines whether it is are or is. More men are is the core of the sentence.
There is more than one man in the room.
Suddenly the verb changes. Has the core syntax of the sentence changed? No: for the sake of consistency, we must say more is the subject and is the finite verb. The phrase than x is still not the head of the subject, no more than in the first sentence (there are more men than just John). If more is the head, then it must be elliptical, since it is only an adjective: more of what? If we hypothetically supply the omitted noun, we get:
*There is more [men] than one man in the room.
There is no other word that we could fill in, though of course this is wrong: *there is more men is both unidiomatic in this register and in violation of the rule that subject and verb must agree.
Then what causes this singular is in there is more than one man? The phrase than x should not determine the number of the verb: and yet it does. That is why this construction is idiomatic, as opposed to regular: it violates the rule that subject and verb must agree. But it is by all means "correct". That is what idiom is: a widely accepted phrase that violates the regularity of our language. However some of us might like it to be, language is just never regular in all respects; this bit of idiom happens to have triumphed over regularity and is now the norm. Idiom must be judged case by case and often varies across registers and dialects.
But could this disagreement of subject and verb be explained away by other factors? Let's see what I can come up with.
It could be that the somewhat fixed phrase there is is what does it. But that phrase could not explain singular is in this sentence:
More than one man is still in the house.
Could this is be explained by the immediate precedence of one man? It is conceivable that the singular number of one man leads us to an anacoluthon in the next word is: we see a singular number and noun, and we cannot resist the pressure of proceeding with a singular verb. But then this phenomenon should not occur if the verb came before the subject:
Not only has more than one man been seen near the power plant, but...
*Not only have more than one man been seen near the power plant, but
It seems clear that have would be wrong, even more so than in the previous sentence patterns. So whether the verb comes before or after doesn't matter.
How can this oddity of disagreement be explained? If we look at it reductionistically, in terms of association and pattern recognition as they occur in the brain, I suspect that the word one exerts such an enormous influence on our perception of a sentence that it overrules more, despite the ordinarily forcing rule of agreement; it does so even despite the sense of multitude inherent in the phrase more than one man as a whole, which must always refer to multiple objects in reality. When we write one man, we have the image of one man at an irresistibly prominent place in our working memory. (Other, somewhat similar idioms exist, so I don't believe this to be a unique situation.)
Best Answer
You question is basically the last sentence of your post:
"What is the right form to use for a pair of, a bunch of, a group of, etc.?"
I think the answer to this is a bit complicated, as it depends on the way the speaker/writer is thinking about the noun phrase. Is it in essence a singular entity, or in essence a plural entity? Thus, the examples given by previous posters are correct, but they each represent a different way of thinking:
The example given by Goos, "There is a bunch of bananas hanging from the tree," is clearly a singular entity being spotted by someone looking at it as such.
The example given by Michał Kosmulski, "there are a bunch of people outside," is different in that it is the people who are the real item here, not the bunch.
Thus, I would say that it is the focus of the speaker/writer which is the essential element here.