The rUK never had a say in it - this point is kinda where things are right now. As of 2011 census the population of Yorkshire, as an example, was just marginally higher than the population of Scotland. Except Scottish people get more money from the treasury and their MPs got to vote on what happens in Yorkshire, the converse largely not being true. It wasn't until the referendum that this situation got the spotlight.
Nonetheless I think in general, as a UK citizen myself, that the British (ie UK citizens, the nomenclature gets convoluted!) consider the Union to be central to UK strength as a nation in terms of society and business and much else (education, sport, language, identity, history, position on the world stage, defence, ...).
Dissent grows though - once the Pandora's Box of the West Lothian Question had been opened and it started to sink in, and we saw that many in Scotland wanted to ditch the rest of the UK and make a run with what they perceived to be vital resources, that I feel rather unsettled people. Why shouldn't the rUK have voted at the same time whether to kick Scotland out of the Union too - that would have only been fair.
Her Majesties government certainly made efforts to retain Scotland in the Union, that could well be key.