The Oyster manual (http://www.babystyle.co.uk/pdf/Oyster_IM.pdf
) shows that the chassis is compatible with at least 7 types of car seats if you buy the right adaptors. Perhaps you could find an alternate car seat to use when you go to ASDA pushing the pushchair, but come home in a car having released the carseat from the chassis.
This is a lot of hassle when you're coping with child, groceries and fatigue, but I can understand wanting to take care even on short journeys.
And before you know it the child just needs a booster seat which you can take along more easily.
Good luck and safe travels.