Well, being pedantic, both the KCL courses you've mentioned are joint honours degrees, and are jointly offered by the History Department (within the Faculty of Arts & Humanities) and by the Department of War Studies (within the Faculty of Social Science & Public Policy). So to say "they're part of of the same faculty" is wrong for a start.
Is your teacher saying that one or the other of these faculties has a policy of only making one offer per candidate? Are are they saying that this applies to KCL generally?
What I
can tell you is that it doesn't apply as a general rule to all universities. I've seen several examples here on TSR of candidates applying to more than one course at the same university and receiving offers from both. I recall one example, where someone was so keen to go to a particular university that they selected one of these offers as their firm and the other as their insurance. There was no issue in them doing so. (
Edit: I've just lookup-up that example, and the candidate selected BEng in Product Design Engineering as their firm and BSc in Product Design & Technology as their insurance - so they were definitely within the same faculty!
)So if your teacher is trying to explain how multiple applications to the same faculty at the same university would be perceived
generally, then they're simply wrong. However, I have no specify knowledge of any policy which may be in place at KCL.
That aside, all four of the universities you've mentioned are very competitive and are less likely to be flexible with grades on result day - so it might be wise to follow your plan to apply to History and Politics at Sheffield as a safety
anyway, simply to increase the likelihood that you'll secure a range of offers, and will ultimately secure a place without dropping into Clearing.