Empire is irrelevant here, as it had very little bearing on the domestic political situation in the UK. Virtually all the British Empire became independent over just a few decades, at the same time that mass de-industrialisation happened domestically. Yet during this period elections still happened in the UK, power changed hands smoothly multiple times, there were no revolutions or coups, and even the IRA was at most an irritant. Despite the loss of empire and the rapid change in the workforce and makeup of the economic output of the UK, it still paid its bills, maintained a nuclear deterrent, integrated a large influx of ex-Empire immigrants, pioneered socialised healthcare in the West, and managed to grow its domestic economy at a reasonable rate almost all the way through. You'd be hard pushed to find another country that was as stable, given the specific challenges over that period.

Brexit was a mistake, and recent governments have been terrible, but don't delude yourself into thinking those are existential crises for the UK. The government will get replaced without much fuss, the UK will patch up its relationship with the EU even if it doesn't rejoin, and the wheels will keep turning.