I think this debate is a lot more nuanced than this post, really. No, prejudice against a person simply because they are part of a particular group is not acceptable. However, it is important to understand the nuances of the relationships between the nations of the United Kingdom.
For example, England colonised two of the other nations and as a result of that colonisation, native languages were crushed (or, in the case of Ireland, actually deliberately eradicated), and other really aggressive policies were put in place. Scotland, while not colonised, was joined with England involuntarily (nobles voted for it, though arguably were coerced due to financial ruin, and it was incredibly unpopular among the people at the time). After the Jacobite rebellion, Gaelic and Highland life were systematically and deliberately crushed by the British (yes, lowland Scots were also a part of that, just as native Indians were used in the oppression of the Indian people during the time when the UK colonised India). My point is that there is some difficult history there, and the UK is founded on relationships that were never equal. Though these things are in the past, they are really only a few generations ago, and these kinds of resentments live on in songs and are passed down for several generations. This is just a natural human thing.
While all of that is in the past, imperialist attitudes do persist. It is simply a fact that the UK is dominated by England, and often people from the three smaller constituent nations do not feel that they have an equal part in what should be a four-nation kingdom. From little things like there being no television for Scottish children for the first three weeks of summer to much larger and more subtle things, like the presentation of Scots on TV up until the late 90s as drunks or layabouts. Or, the eradication of Scots due to the imperialist attitude that only Standard English is correct. There are many, many, many things, from the obvious to the subtle, that cause these relationships to be rather prickly.
So, no, nobody should ever be prejudiced, but it is important to understand the reasons why people often feel the way they do. If more was done to really address these often imperceptible concerns then there would be more hope of actually saving the UK. (And I say imperceptible, as a lot of anger in Ireland/Scotland/Wales comes from people feeling like their identity, culture and worth are ignored or trodden on but not being fully aware of why they feel this way). Sadly, the Tories seem hell-bent on deepening these rifts, not mending them, so I suspect the chasm will only get bigger.
On a slightly lighter note, maybe your neighbour was just pissed off at the influx of visitors! When I lived in Edinburgh, lots of people used to curse the "bloody Americans" during the festival, but it didn't mean they were prejudiced against Americans - they were just annoyed at the influx of them to their city that meant they couldn't go about their daily business as usual!