One of Mr Bean's quirks is that he hates this particular three-wheeled car:
My question is then, do we know why he hates this car? Has Atkinson or any of the writing staff ever commented regarding this hatred?
It's a meme.
In the UK, everybody hates those cars.
Google refs: Jeremy Clarkson/Top Gear, Reliant Robin or Reliant Supervan; Only Fools & Horses.
Try this Youtube video to see Clarkson "testing" one -
Even the members of the owner's club in the Top Gear video are quite aware of how bad their cherished vehicles really are.
Seriously, they were actually quite dangerous, unless you kept additional weight on the passenger side.
Their fibre-glass construction also made them deadly in any crash.
They were popular, really, only because you didn't need a full motor vehicle driving license to drive one unaccompanied, you only needed a motor-cycle license.
This is the "Supervan" variant, made [in]famous by Del-Boy & Rodney Trotter, in Only Fools & Horses.
The meme already existed by the time this show was first made in 1981, the abysmal quality of the vehicle adding to the characterisations of the protagonists.