The right certainly seems to have come to dominate the Conservative Party since the referendum -- maybe always there but kept down a little under Cameron and Osborne. And Labour has certainly moved considerably to the left since the days of Blair and Brown. So there is nothing left in the centre for those of us who would like a centre-slightly-left or centre-slightly-right party to be able to consider voting for.
The right were dominating the Conservatives under Cameron and Osborne, they were many things but centrist they were not. Economically Cameron and Osborne were far-right, privatising everything, pulling down the welfare state. Their agenda was, and is, heading well towards libertarianism.
The legalisation of gay marriage was the positive side of that libertarianism, but don't confuse it for centrism.
May's record as Home Secretary showed the more authoritarian side of the right-wing of the party, vilifying foreigners and poor people. The restrictions on work permits, deporting people who earn less than £35,000, the "racist van", the abolition of the Border Agency. The creation of the Border Force and Immigration Enforcement, and the psuedo-military insignia and uniforms that the two bodies now have, just sums up where the Tories were and are going.
It's that authoritarian side of the party that are in the ascendancy now. Cameron was socially liberal but economically far-right; May appears to be much more socially authoritarian but economically more towards the centre.
ETA As for Labour, I genuinely don't think they have moved that far back towards the left after Blair. Both Corbyn and Miliband have been targeted as "communists" but neither of them are: Corbyn's "Trotskyite" manifesto wasn't noticeably different to that of the SDP under the Gang of Four. I know people like to compare him to Michael Foot, but the truth is very different. Economically Corbyn is very much in the centre ground, but he is liberal when it comes to law and order, etc.
Cameron's talent was pushing economically far-right ideas through under a veneer of centrism, and Blair's talent was pushing economically left-wing (Sure Start, minimum wage, tax credits) ideas through as centrist. Blair was never as right wing as people believe, and Cameron was never as centrist as people believe.