First, many workers were supporters of the Liberal and Tory parties, which opposed nationalisation, and many more workers were indifferent to politics, and whether industry was nationalised, and indeed many worked in small, unorganised trades, where the question hardly arose (see Gareth Stedman Jones on Outcast London).
Among organised labour and the left there was general support for some kind of collective organisation of industry, but since it was largely a theoretical question, the difference between the *nationalisation* (i.e. state ownership) of industry and the *socialisation* of industry (i.e the transition from a free market to a democratically planned society) was not well understood. Engels made the point in the debates of the First International that socialism was not the same thing as nationalisation - 'otherwise Bismark's government owned tobacco plants would be socialism' (not verbatim).
When the state did start to organise and even take ownership of selected industries in the first world war, organised labour did embrace nationalisation as a general programme, investing great hopes that the government (which they felt they could influence) would guarantee their interested better than private owners, who they despised in a way that would be surprising to hear today.
A few militants, like Noah Ablett (author of the Miners' Next Step manifesto) did oppose nationalisation, on the basis of Engels' distinction, but that was very much a minority view. On the right, of course, workers affiliated to the Conservative party would continue to oppose nationalisation.
Postwar, some Trotskyists like Ken Coates fudged the issue with the demand nationalisation 'under workers control' which did have a resonance, because rank and file workers had experienced the nationalisation of the coal industry as the exchange of one set of bosses for another, and the Institute for Workers Control was an interesting, but probably marginal pressure group throughout the sixties and seventies.
In the second wave of nationalisation - and even the creation of workers cooperatives - in the 1970s (a last-ditch attempt to save some failing industries) again the core of organised labour was in favour, but there were some radical critiques of nationalisation. In my hand I have a copy of 'State Intervention in Industry: A workers enquiry' (1980):
'In Britain, at least, socialism has usually been associated in most peoples' minds with increased state intervention. Many socialists have also emphasized workers' control and popular power but this emphasis has never been strongly enough supported or practically enough worked out to shape the popular image of socialism.'
Alas, it was no more practically worked out in the 'workers enquiry', which was, at any rate, written shortly before the policy was being thrown into reverse by Mrs Thatcher, with her policy of privatisation of nationalised industries (which, let it be said, was popular with many workers, though not as a rule with trade unionists). On the left, all distinctions between nationalisation whether or not under workers control, still less Engels' 'socialisation' were lost in a rearguard, and mostly unpopular campaign to save the nationalised industries (though the campaign against pit closures and in defence of the NHS were popular)