They can and there's plenty of evidence for that from other governments. Trade union membership is key, power in society is grossly disproportionately wielded by those at the top. Under a proper trade union framework, like exists in the Nordics and Germany, unions will act as a counter weight to that power.
but you oppose all the other public sector changes in those country, you know, like the ones the coalition are trying to bring in...
Then there are other things that have worked in promoting equality in other countries, like protecting your key industries (every country does this except us) and subsidising food production to ensure a viable rural economy.
And school selection, private provision of state funded services, concentrating on access rather than provision and so on...
Yes inequality got worse under Labour, but at least they tried to do something and didn't pretend inequality wasn't an issue. At least they did manage to slow down the rate of inequality growth.
Depends on what metric you use. They slowed down income poverty by lifting a significant number of people from just below the arbitary level to just above it. Social mobility, on the other hand, suffered an increasing growth rate.