Pride in your country, it’s traditions and culture is perfectly natural and healthy.
There is no requirement for any particular group of citizens to claim this. It can and should apply to everyone and that’s what everyone should be striving for.
Unfortunately “English Nationalism” has been hijacked by xenophobes with the intention to divide, rather than unite.
I can't really see how you can be nationalist without wanting to maintain a nation. A nation is hardly just a border on a map. The people have to all be a part in it. Clearly, parallel societies exist, whether wanting to replicate some kind of other lifestyle or alliance knowingly, or simply by circumstance. A nation is language and culture etc. It really can't just be whoever accidentally lives there. That's the road to former Yugoslavia and Balkanism. People living in states but not their nation state - as they see it - some actively fighting against it. Sound familiar at all to anything you see?
Cornish Nationalism would hardly just be an independent territory of Cornwall - it would be Cornish speaking with Cornish traditions. Wales similarly. Not quite the same in Scotland where there has been English speaking parts for a thousand years or so and Scots Gaelic seems to not have the allure of Welsh or Irish, or even Cornish in Cornwall. England would be English language and culture, that's what the education system would teach and encourage. That sounds almost impossible now - certainly highly unlikely.
Something like 20% of the population across pretty average places in England (not Bradford or Hounslow or anything ridiculous) filled in the last census saying that English is not their spoken language. As for traditions, half the people don't even know them anymore and they are often frowned on now, by English people as much as anyone else. I can't help but feel England and Europe are a victim of believing their own theories on colonialism and integration whilst ignoring any actual evidence, or longstanding social, political and psychological theories and studies - which are there for anyone to see, if they can be bothered to look. Group dynamics, migration, immigration, integration, crime, language, psychology. Since at least the fifties, studies have found similar things. Even when approaching issues from different lenses or political theories. Integration has been problematic to say the least. Really the political approach just shows the same people divided but blames different reasons for it. The original research found the divide - it's there. We just argue over why now. For one side it's someone else's fault, for the other it's their own fault. Where you stand on the political divide will define which side, left or right, would think that. So that can give you a bit of a laugh with people.