I'm in this situation. Builders coming to my street (small cul-de-sac) to move bulky building materials to a property that is located on neighbouring street and its garden backs onto my street. They destroyed some vegetation on my street to create a pathway and opened up part of a fence. There are builders' vehicles coming to my street. Can I legally stop them from doing that? I also have been sworn at when I was taking pictures of their vehicle and company logo.
Summary: More information needed, but I have listed out some legal claims available to homeowners when they have similar concerns.
There are several issues here which need elaboration before deciding if you can take legal action.
The first is: "the destroyed some vegetation on my street."
If the by "my street" you mean that the street is part of your property, you may sue the builders for trespass and/or damage to property.
If the street isn't your property, but the vegetation is your property, you may sue them for destruction of your property.
What you are probably looking for, however, is a prohibitive injunction. This is a court order forcing the builders to avoid doing something, e.g. An order forcing them to avoid using roads adjacent to your property.
To obtain such an injunction you will have to prove that what they are doing is violating your rights, is somehow harmful to you or your property, or inevitably will do either of those things. One way to demonstrate this is if you can show that you have a claim under nuisance, or damage to property, or trespass.
On the description you have given us, there isn't enough to say your rights are being violated, or that your property has come to harm or will come to harm because of their actions.
You should also be aware of claims under nuisance. Nuisance is when someone is doing something that prevents you from "peaceful enjoyment of your land".
It appears from your question that the actions of these builders have, in your mind, done this. However there are several aspects that have to be satisfied for this to amount to private nuisance:
What the builder are doing must be a "continuing state of affairs." They may have annoyed you by trampling over vegetation, but if this is a "one-off" event, it is unlikely to amount to nuisance.
A reasonable person must find the conduct to interfere with the enjoyment of their land. That is to say: it isn't enough that their conduct is making you unable to enjoy your land peacefully, you have to show that any reasonable person in the same situation would find this conduct unacceptable.
Finally, the context of your neighbourhood matters: if the behaviour is something expected in a residential area, then it will not amount to a nuisance. For example, heavy drilling in an industrial location will not amount to a nuisance, while the same may do so in a normally quiet neighbourhood.