Anyone who sets out to classify anything soon finds that not everything fits into the neat categories he has devised. Whilst zoologists and botanists do not exactly have an easy time (zoologists thought they had mammals sorted until they learned about the duck billed platypus) the classification of languages at certain levels is tricky because there are not necessarily discrete entities. Linguists like to talk about dialect continua. They say things like: "There are only dialects". Even so, there comes a point where there is a break in the continuum. "Dutch" and "German" are both south Germanic languages and there is a continuum of dialects between them so that at one level it is difficult to say that "Dutch" and "German" are different languages. You can of course decide that if an idiom has certain features it is "Dutch" and if it has others that it is "German", but there is bound to be some idiom that shares the features you have chosen as being typical of "Dutch" on the one hand and "German" on the other. "Danish" is a north Germanic language and there is a no dialect continuum between Danish and any language that could be called "Dutch" or "German". So, it would seem that, at least provisionally, we could talk about a "north Germanic" language and a "south Germanic" language. But, within north Germanic whilst there is a dialect continuum between the Scandinavian languages, there is no dialect continuum between the Scandinavian languages and Icelandic. Within south Germanic there is a break between the Anglo-Frisian idioms and the other south Germanic languages. When we get to the Anglo-Frisian idioms there is clearly a break between the varieties spoken in the British Isles and on mainland Europe. Despite all these breaks, all Germanic languages have something in common that justifies them being classed as Germanic and quite distinct from Slavic, Celtic and Romance. Moving further up the scale, all Indo-European languages can be shown to be related.
If we turn to Britain there is a dialect continuum as you move from the south coast of England northwards to the Lowlands of Scotland. On your journey you will move from a zone where the idioms may be classified as "Southern English" to a zone where they may be classified as "Northern English" without perhaps necessarily realising when it happened. As you continue, you will find yourself in a zone where the idoms may be characterised as "Scottish", but the boundary between Northern English and Scottish idioms does not follow the political/administrative boundary between England and Scotland. By the time you get to, say, Ayrshire and compare the idiom with the idiom of, say, Brighton, you may start to wonder if there is a justification for classifying the two as separate languages. In fact the situation in (southern) Scotland is quite complex. On the one hand there is a variety called "Scottish English" which is distinct from, but close to the variety often called "Standard Southern English", and on the other "Scots", a variety that has a good claim for being called a "language" whatever we decide a language is. Many speakers move between "Scottish English" and "Scots" and there is no point at which the two can be separated.
So, when we look at the varieties of Germanic idioms spoken in Britain we find both homogeneity and diversity. Is everyone speaking the same language? In certain situations, linguists avoid making a distinction between language and dialect not least because these terms can can carry political and other overtones, but also because the distinction between a language and a dialect is a comparative one. Even if one decides that there is a language A divided into dialects A1, A2 and A3 and another language B divided into dialects B1, B2 and B3, it does not follow that the distance between A1 and A2 is the same as that between B1 and B2. For these reasons and because the phenomenon of language cannot be fully studied or understood except in a social context, linguists have had a problem in coming up with taxonomic categories equivalent to the biological "class" "order" "genus" and "species" (which themselves are not without their problems) and when they do come up with them, of naming them.
I suspect that the question posed is not so much concerned with the varieties of "English" spoken in the British Isles, but with the notion of "Englishes". I think this term is used to describe the varieties of English spoken throughout the world, so that we talk about "Indian English" or "Malaysian English". I think this is useful to the extent that it emphasises that all these varieties are equally valid and that outsiders should not seek to impose their own standards. It is fraught with danger to the extent that it encourages fragmentation. It is of course in the nature of language that it changes. However, it is important to remember that language is above all a means of communication. If a group wishes to adopt a language they are perfectly entitled to do what they want with it, but if they play around with it too much, they should not be surprised if they are not understood outside their group.