"Tradition" means a continuous, transmitted process. The style that's been transmitted to you is Irish. The fact that you're English, living in England, doesn't alter that, and doesn't make it English.

Many tunes are common to all the traditions of the British Isles, and often the only thing that distinguishes them is the style in which they're played.

Whilst there aren't as many recordings around of traditional English fiddlers as there are of Irish, you should be able to find enough for you to get an idea of the style. Fiddle styles vary around England (just as Irish fiddle styles vary from region to region). "English sessions" often mean southern or East Anglian music, but the north has its own style and repertoire.

I'm not a fiddler, so I can't be more specific than that. But if you want to play English music, learn to play an English style.