No, Charles will become King of the United Kingdom of Great Britain and Northern Ireland, along with 15 other Commonwealth Realms the moment his mother dies. England stopped being a separate kingdom in 1707. Anne Stuart was the last English monarch. The Acts of Union of 1707 ended the separate kingdoms of England, Scotland, and Wales to form one united realm. It isn't pedantry to give correct, full information about the proper titles as some rabble-rousers like to say, rabble-rousers who are all for being ignorant of full facts. England is only part of the realm, and to mention only England is to forget Scotland and Wales.
Camilla, as the wife of the king, automatically becomes Queen CONSORT, the non-reigning spouse. Spouses don't have hereditary powers to reign and are there to support the monarch.
The Coronation is a solemn blessing service of the monarch that takes place about a year after the death of the late monarch. The service brings the kingdom together for prayers, not just for the new monarch and spouse, but for the realms. It's more than a mere formality but a symbol for unity, connection.