It's a term left wing shitposters in the UK use to describe what we could call "the moderates" or "centrists." It's useful because it distances from any positioning on the ideological spectrum as there is nothing necessarily 'centrist' or 'moderate' about their politics. Sensibles is ironic, of course, as there's nothing sensible about them, but being Sensible, the belief that they are the only people who should be in charge, is core to their self-perception and, more importantly, how they are portrayed by political journalists.
Being sensible, they can never be wrong and their critics can never be right. They almost always get exacly what they want, and the resulting horrors are then everybody else's fault. The Squad, "defund," whatever.
Anyway, our Sensibles are at it again. They have been sabotaging the Biden agenda for the year, succeeding, and somehow this and everything else is the fault of The Left. You know, inflation is the fault of BBB which didn't even pass because they sabotaged it.
