It's a genuinely good question, so here's my take on being English for what it's worth.
Recently I've done a lot of family tree research and it transpires that I am equally of Scottish, Irish, Welsh and English pedigree (in no particular order ) Indeed my great grandfather x 3 was born in Ireland, married an English girl and was decorated for deeds at the battle of Waterloo, this doesn't make me want to be Irish though or indeed in any way jealous of the Irish. My Grandmother was a Scot and I loved her to bits, at the same time I am proud of that connection, however, I was born in England, raised in England and I AM English. I can't tell you that I feel proud to be English because of Winston Churchill or any one other thing, it's just that it's where I'm from and I'm proud of it. Yes we maybe seen as the "Millwall" of the UK, everyone hates us, or at least that's what the other constituent parts of this nation would have us believe but I think in some ways that just makes us even more bloody minded and proud.
At the end of the day the UK is a fairly special place to hail from and when push comes to shove, as a combined unit, we are certainly no pushovers. So in summary, like may others, I suspect, I am proud to be British and proud to be English/Welsh/Scottish/Irish. One thing I would add is this, I'm 58 and as a kid/young man I was always proud to be British, now I think more than ever I feel more proud to be English and I think that stems from the overt individuality of the other nations, in some ways I think this pushes us to be more "English" than perhaps we used to be. It would be interesting to know how others feel. Sorry for the ramble but hope it makes some kind of sense.