Most cars have two tyre pressure levels - 'normal', with likely up to 2/3 people in the car and nothing in the boot, and 'fully laden' with 5 people and a boot full of luggage or other heavy items.

An average person weighs between 50 - 75kg (roughly translated into 'old money' as 8st - 12st), so your scooter is the equivalent of one person, though the vast majority of its weight will be distributed over the rear axle, probably the equivalent of two people sitting on the back (where some weight is distributed over the front axle as well as [mainly] over the rear).

Given you are also carrying the hoist, which may be, say, 15-20kg by itself, you may wish to pump the rear tyres up a bit above the 'normal' pressures if its just you in the car, maybe to 33 - 35 (assuming the 'normal' tyre pressure is 32psi all around), and possibly the fronts by 1psi. You may need to adjust this if/when you carry more passengers (depending upon where they sit), but its probably best to generally make the changes in small increments to see how you get on - especially where handling (you don't want the rear to be too 'light', particularly in the wet) and tyre wear (uneven tyre wear should be avoided for safety reasons) are concerned.

To be honest, having smaller wheels/higher profile tyres is often the answer (I don't know whether you had the option to have 17in or 16in equivalents on your car when you bought it), though swapping out one set of tyres for another with a softer compound (HJ likes the all-weather Michellins) can help to a degree as well, though they won't last as long as they wear quicker due to the compound. It might (if you don't want to change wheels and tyres or can't afford to, given you've just bought it and have 4 perfectly sound new tyres) be worth considering these options when you do need to change tyres down the line, if the tyre pressure changes work to some degree, but not enough in the long term.

Thank you for your thoughts on this. Because this is a Motability vehicle I cannot choose/change wheels as I might well do if it were my own.

When the scooter is loaded it faces front to back (the back seats have to be lowered to get it in) so some weight is distributed towards the front. I think I will try 34 psi and see how it goes from there.

Car tyre pressure specifications usually have a good safety margin (particularly for the lighter load recommendations) so the "comfort" pressures would probably be OK in this instance. However to have total confidence and to avoid problems with police/insurers etc in the event of an incident, a pressure increase might be advisable. Guessing that we are considering 215/55R18 tyres with a 95 load rating, a 2psi pressure increment will increase axle load capability by 65kg. Add another 2psi and the axle load capability will be 130 kg above that at the comfort" pressure. Adding 2psi to the rears only may be acceptable, but to be extra careful go for 2psi more in the front tyres and 4psi more for the rears.