Analysis
There now seems at least a possibility (again) that Scotland might withdraw from the United Kingdom. Leaving aside what “Independence” means for Scotland in this context, let us examine what it means in practical political terms for England and the rest of the British Isles.
The present House of Commons has 650 Members (to be reduced to 600, possibly by 2020). 330 are Conservatives, 230 Labour (229+1 vacant seat last held by Labour), SNP 54, Liberal Democrats 9, Democratic Unionist 8, Sinn Fein 4 (in abstention; do not vote), Plaid Cymru 3, SDLP 3, Ulster Unionists 2, UKIP 1, Green 1, “Independent” 4 (being MPs such as Simon Danczuk who have had the whip withdrawn), Speaker 1.
It will be seen that while the present Conservative majority is notionally 11 (leaving aside the Speaker, who votes only when there is a tie), Sinn Fein do not attend or vote, so the real majority is 15.
If Scotland leaves the Union, the 650 MPs in the House of Commons will have their number reduced by 59, of which 54 are SNP, 2 SNP MPS but who are suspended (and under police investigation) and 3 LibLabCon (1 each). It can be seen that, on the pure mathematical basis, that would mean that the Conservatives would have, on present figures, 329, with all other MPs (except Sinn Fein and the Speaker) numbering 257: Conservative majority 72.
Most of the Westminster seats presently occupied by SNP MPs were, until 2015, Labour seats, so it can be seen what a mountain Labour would have to climb to replicate its Commons strength or anything like it were Scotland to break away from England, Wales and Northern Ireland.
That, however, is not the end of Labour’s catastrophe. The reduction of Commons seats from 650 to 600 is expected to reduce Labour numbers by as much as 30 in any case and to almost wipe out the Liberal Democrats. If that were to be so and if the 59 Scottish MPs were not there, then the Commons would be 541 and might be about 310 Conservative, 200 Labour, 26 others (plus Sinn Fein -4- and the Speaker). Effective Conservative majority of 74.
Labour is at present polling at about 25%. There is no obvious reason why Labour should do markedly better any time soon and certainly none to expect a vote percentage much above 30%. That would, on the new boundaries, probably give Labour about 150 seats, possibly far fewer. It is not impossible that Labour could end up with as few as 100 seats out of 541. However, even if Labour were to have 150 seats out of 541 (effectively, out of 536), that would make Labour little more than a niche party, albeit with the title “the Opposition”.
The existence of the SNP in the House of Commons gives declining Labour the hope that the next general election might provide at least the possibility for a Labour minority government of some kind, with tacit SNP support, assuming that Labour could at least somewhat improve its position electorally. Without SNP MPs in the Commons, that slim hope is dashed and Labour broken with it.
Speculation and Hope
If, sometime around 2020, the Conservative Party has maybe 350 MPs in a 541-MP post-boundary changes, post-Scottish Independence, post-Brexit House of Commons, England (plus Wales etc) becomes a one-party state in all but name. Elected dictatorship. The only hope then for positive change will be the emergence of a new movement based on social nationalism, the only ideology which can unite England as a country and as a people, meaning at least the 85+% who are white Northern Europeans, together with those willing to accept European culture.
Update: Further Thoughts (drafted 23 July 2018)
Scotland fairly narrowly voted not to leave the UK, of course. The SNP still dominates though its cadre of Westminster MPs now numbers, after the 2017 General Election, 35 (strikingly down from 56 in 2015; the 2010 figure was 6). The opinion polls have for some time been both against a second Independence referendum and against breaking away from the UK.
Meanwhile, Labour has regrouped under Jeremy Corbyn and has at least managed to halt what I saw a couple of years ago as its possibly terminal decline. The incompetence of Theresa May and her Cabinet has weakened the Conservatives, though both large System parties are quite close in the polling as I write.
The House of Commons still has 650 MPs. The Boundary Commission report indicates that the number will be reduced to 600 by 2022, of which number 499 will be in England. While the changes favour Conservative over Labour, they will not come into effect until 2022, whereas the next General Election will probably be earlier, possibly even in 2018, though most commentators think 2019.
The SNP are still likely to be potential kingmakers after the next General Election, but that is not as likely as it looked a year or two ago. At present, the Conservatives cling on by grace of the DUP’s 10 MPs. The SNP can only snipe from the sidelines. It now seems not impossible that, in a close general election result in 2018 or 2019, Labour might emerge as the largest party in the Commons, under the present boundaries. It would then need SNP MPs’ votes in order to govern at all.
Update, 20 June 2020
Well, water under bridge etc…
The Scottish public’s view on “Independence” is now volatile, but the most recent opinion poll (June 2020) has the pro-“Independence” vote as 48% and the antis at 45% (Undecided = 7%). Without the Undecided, the result would be 52%-48%, the same margin as the UK Brexit Referendum.
As for the reduction of MP numbers, the Boris Johnson government elected in 2019 has decided to ditch the change. There will be 650 MPs in the House of Commons for the present.
The result of the 2019 General Election in Scotland: https://en.wikipedia.org/wiki/List_of_MPs_for_constituencies_in_Scotland_(2019%E2%80%93present)
If Scotland chooses to leave the UK, the number of MPs left at Westminster will be 591. At present there are only 6 Scottish Conservatives, 4 Scottish LibDems, and a sole Scottish Labour MP, but also 48 SNP MPs.
The Conservative Party would have 359 MPs, Labour 201, LibDems 7. The Conservatives would be one seat worse off than they now are, so the effect on their Commons majority would be minimal were it not for the absence of the (at present) 48 SNP MPs. Overall, the Conservatives would be, therefore, 47 MPs higher in terms of majority. That would, on present seats, give the Conservatives an unassailable Commons majority of 127.

Update, 9 September 2018