In giving the Hugo Young lecture Nick Clegg (reprinted here on Comment is Free) contrasted the 'new progressive' outlook of the Liberal Democrats with Labour's 'old progressive' approach. The former 'focus on the power and freedom of citizens' while the latter 'are straightforwardly in favour of more state spending and activity'.
In doing so Clegg arouses the ire of Jonathan Calder: 'Nick Clegg should speak about liberalism not "progressivism"' who endorses the view of Contrasting Sounds that 'the word “progressive” should be taken outside of UK politics and shot. Or rather, restricted to its technical meaning in tax discussions.'
I don't disagree with Jonathan's conclusion that this is really about the 'contrast between liberalism and socialism. Yet the term progressive does have a meaning in British political tradition beyond a narrow one about the tax system. In the Edwardian era (and possibly before), Liberal politicians were in the habit of using the term 'party of progress' as a generic description for their own party and their Labour allies. This contrasted with the Conservatives whom they saw as the 'party of reaction'. On the London County Council after its creation in 1889, the Liberals worked within a broad grouping that included Labour and socialist elements which contested elections under the 'Progressive' label. And historians are in the habit of referring to the co-operation between the Liberals and Labour before the first world war as the 'Progressive Alliance'. (Although my brief online trawl of contemporary publications suggests that this term may not have been widely used at the time.
Whether in a historical or modern context, the word 'Progressive' is still a useful generic term to distinguish those who, regardless of party, see their political outlook as being about championing the poor, the excluded and the disempowered against the established order. So I suppose that in addressed a Guardianista audience, Clegg is referring to 'Progressivism' in order to make the case that Labour don't have a monopoly of such sentiments - we share them but have a different approach to achieving them.