Complaining about globalization is as pointless as trying to turn back the tide. There are, I notice, no such debates in China. They are not worrying about potential threats but are busy seizing the opportunities in ways that are transforming their society and ours as well.

And here’s what he said back in 2000:

There is no new economy. There is one economy all of it being transformed by information technology…What is happening is no dot.com fad that will come and go – it is a profound economic revolution.

2. Both Marx and Blair believe capitalism radically transforms the world. Here, famously, is the Communist Manifesto:

The bourgeoisie cannot exist without constantly revolutionising the instruments of production, and thereby the relations of production, and with them the whole relations of society…Constant revolutionising of production, uninterrupted disturbance of all social conditions, everlasting uncertainty and agitation distinguish the bourgeois epoch from all earlier ones. All fixed, fast-frozen relations, with their train of ancient and venerable prejudices and opinions, are swept away, all new-formed ones become antiquated before they can ossify. All that is solid melts into air.

And of course, pretty much any Blair speech talks about the newness of something or other. David Marquand cites him thus:

‘New, new, new’ Tony Blair told a meeting of European socialist leaders in a characteristic outburst shortly after entering office, ‘everything is new.’

3. Both believe history follows a law-like path – it’s not just one damn thing after another. This is obviously Marx’s view. It’s also Blair’s. New Labour policies, he claims, are rooted in an understanding of the forces shaping historical change. Here’s Marquand again:

The world is new, the past has no echoes, modernity is unproblematic, the path to the future is linear. There is one modern condition, which all rational people would embrace if they new what it was. The Blairites do know. It is on that knowledge that their project is based.

Alan Finlayson is also good on this. He shows that New Labour has many of its origins in Marxism Today’s “New Times” analysis in the 1980s, and continues:

The Third Way forms a politics based on the fallacy of empirical sociology – that social trends are always clearly identifiable and neutral phenomena as long as you have enough statistics.

Now, you might object here that there’s a big hole in Blair’s Marxism – there’s no revolutionary politics.
This complaint rests on a misreading of Marx. He wrote:

No social order is ever destroyed before all the productive forces for which it is sufficient have been developed, and new superior relations of production never replace older ones before the material conditions for their existence have matured within the framework of the old society.

Blair obviously believes that capitalism has not yet finished developing the productive forces, so revolution would be premature.
There’s good evidence on his side. Profit rates are still high – the tendency for the rate of profit to fall hasn’t asserted itself. Productivity growth in the most advanced capitalist country is strong. And the numbers of new patents (though an imperfect measure) suggest technical progress is still rapid.
What’s more, the working class is not yet ready for revolution. There’s little demand for the key Marxist  ideals of the withering away of the state or greater autonomy at work. The working class is not yet a class for itself.
As revolution would be premature, Blair seems to see his task as helping capitalism develop the productive forces. Hence policies such as tax credits and education to increase the labour supply, and generous PFI contracts to uphold profitability.
This in turn helps answer another question: if Blair’s a Marxist, why doesn’t he hint at being one?
To do so would be counterproductive to the goal of developing capitalism’s productive forces; capitalists would see such a statement as a threat of expropriation and cut investment. It would be mere childish posturing.
Now, I’m not saying here that Blair has consciously and deliberately adopted historical materialism. But so what? As Marx said, “one does not judge an individual by what he thinks about himself.” All I’m saying is that, in policy terms, there’s more evidence that Blair is a Marxist than that he’s a Christian.