I genuinely think he probably was. I think he was – and remains – ideologically closer to the Left of the Conservative Party than he was to Old Labour. Like many on the Left of the Conservative Party (One Nation Tories), his instinctive preference was for the private sector over public ownership, but tempered by a willingness to accept some, albeit limited, State intervention to prevent ‘market failure’ (Thatcherites, by contrast, seem unwilling to accept that ‘the market’ could fail, believing it intrinsically superior to public ownership) or secure a degree of social justice.
He was a great admire of many business leaders, and viewed them as ‘wealth creators’ upon whose investment and profits British people ultimately depended for employment and growth, and whose taxes helped fund public services. By contrast, Blair seemed uninterested in trade unions – viewing them as an embarrassment, or an ancient relic – and although he presided over the introduction of a statutory minimum wage, he also accepted (like most Conservatives) the need to maximise ‘labour market flexibility’, which meant keeping workers' rights to a minimum, and not restoring to the trade unions any of the rights or powers they lost under the 1979-97 Conservative Governments.
He (and New Labour generally) also believed that the public sector needed to accept private sector involvement: hence the increasing number of private firms involved in health care and provision, and the involvement of business people in helping to establish Academy schools. The introduction of tuition fees can also be viewed as a Conservative-type measure, whereby the users of a service pay for it rather than it being funded out of general taxation. Equally ‘Conservative’ was Blair’s notion of students as ‘consumers’ who would then shop around for the best university or degree, based on criteria such as value-for-money, and his apparent assumption that the primary purpose of university education was to serve the needs of the economy and employers, rather than higher education having any intrinsic social or cultural purpose.
He did, however, lead the Labour Party to an unprecedented three consecutive election victories (two of them landslides) by appealing to Middle England and attracting many disillusioned moderate ex-Conservatives. Also on the plus side, his governments enacted the minimum wage and working-families tax credits to tackle poverty among the working poor; invested more money into public services after years of Conservative neglect; secured the trust of many business people who had hitherto been terrified by the prospect of Labour governments; and promoted cultural and social pluralism (accepting gay relationships and partnerships that were abhorrent to many Conservatives).
Much of the Labour Party, particularly the Left, hate Tony Blair precisely because they suspect him of being a Tory at heart, or at least of sharing many Conservative attitudes and values, particularly on economic issues; his apparent adulation of the rich and big business; his refusal to raise taxes on the better-off due to his assumption that these are wealth creators (rather than the workers who actually make or produce things, or provide services); and the transformation of hospitals, school and universities into quasi-businesses, which can be managed and treated as if they are no different to supermarkets or factories making widgets. They also, of course, hate his pro-Americanism, as symbolised by the Iraq War.