I would submit the chargeback dispute via the website. In this case, the critical detail is that the TA represented itself to be UA. In your OP, you state, "So I called this phone number and they pretended to be United Airlines." That misrepresentation is sufficient to justify the chargeback even if the TA otherwise performed all services requested.
Chances are that the TA will never respond and is more than satisfied with however many scams it has gotten away with and will show up tomorrow as somebody else, somewhere else and under a separate phone number. But, if the TA does respond, it is important for you to have made the express point and in writing that the TA identified itself as UA.
These guys likely have a hundred shell companies ready to go and locations elsewhere to claim as their office (this one appears to be a hair salon in Edinburgh), so the issue is not a warning about this outfit. Rather, as you properly point out, the critical point when you call is to assure that you have located a number on united.com and not some other URL.