While it's true that Scotland has been the preserve of Labour, the Liberal Democrats, and SNP, who are more progressive than the Conservative party, even though in 2015 the SNP won almost all of Scotland they still only have 56 seats out of a parliament of 650, and Northern Ireland has fewer still. Scotland contributed 1 MP towards the Conservative party's majority of 12, but even if Labour, the SNP, and what was left of the Liberal Democrats formed a coalition they'd still be 35 shy of the Conservative total.
Scotland is an at best minor political force as the lion's share of the votes come from England. And even with almost total rejection of the Conservative party from Scotland in 2015 the Conservatives still won a slim majority. However, if Scotland left the UK the remaining parliament would become decidedly more right wing, and it would be easier for the Conservative party to win in future. Even though Scotland is unable to thwart a Conservative England, they still help change the colour of the debate by just showing up.
I'd also like to stress that Northern Ireland is absolutely not left wing. Northern Irish politics is split down the middle between two tribes: Irish catholic nationalists and British protestant unionists. What this means, is that whilst the largest nationalist party is Sinn Fein, whose roots are far left, Catholicism is a pillar of Irish identity which acts to temper their otherwise progressive instincts. The country's attitudes are decidedly traditionalist. Especially the conservative evangelical attitudes of the proudly protestant Democratic Unionist Party... who are generally in an intense state of denial about everything that has happened since 1690. The DUP are a loyal Conservative ally, whilst Sinn Fein are abstentionists, meaning they refuse to attend parliament (because it is a British institution and they are very much not British) and so are of little use to any potential allies in Westminster.