No, the union is stronger together, particularly the mainland. We don't need more reasons to be insular, we don't need an even bigger mess than Brexit - and frankly, what is 'English' anyway?
Am I? My dad is Scottish, my mother's family, Irish. I could have an Irish passport if I wanted one; I'll definitely be able to apply for a Scottish one if we keep close to current rules and we do split. My cousins on my mother's side are Irish/Welsh. None of us would meet 'English' citizenship requirements in the event of a dissolution - although we were born in England and live here, none of us have an 'English' parent or grandparent.
And yet - mum's family moved when she was tiny. So did dad's. Neither of them remember living anywhere else. Superficially, neither of them have an accent other than North West English. I (and my cousins) were born in England and have never lived anywhere else.
Assuming a similar position to that of EU citizens now in the UK, I'd be applying for a passport from a country I've never lived in, which - if I tried to move there - would not recognise me as a native - and then paying for a visa to continue living in the country I was born in. I'd have to prove I had this visa to continue to be legally allowed to work in a role I've had for 12 years. The alternative would be English citizenship via the spousal route, but I'm not an immigrant and the cost of that is 1000's and 1000's of pounds.
This isn't the EU, which has only been around for a few decades, and where there are people alive who remember it not existing. The implications run through everything. It would take decades to unpick it all, and the cost and the time would be horrific. The consequences for 100's of 1000's of people, of all nations, of ripping away national identities and right to live and work, would be horrific.
For what?