The hipness quotient, whatever there is of it, of the PT Cruiser derives from its having been consciously styled to evoke American, '40’s-era station wagons and panel vans, which in turn underwent a revival as hot rods and surfer’s rides in the '60s. I personally think Chrysler’s stylists botched the front-end look badly (I guess it wouldn’t have been Chrysler enough if they made it look more like the classic '40 Ford), but from the A-pillar back I find nothing to criticise in the design.
As someone else said, they’ve been fairly popular in the US, a) because they have a somewhat ‘hot rod’ look with greater refinement and at a price much lower than one would ever pay for a custom job; and b) because they are fairly roomy inside for what, in the US, is considered a small vehicle.
I drove one once as a rental and it was OK, but nothing special, to drive and quite posh inside; really just an economy car with stylistic pretentions. Other than general shape, there is no correspondance whatever between a PT Cruiser and a Black Cab; the PT has a FWD drivetrain, for one thing.
I take it the OP is not in fact located in the UK, as this car has apparently been available there for some time.