Every day except Sunday the Wilsham Road is an all day car park. There is just a five minute walk to town from this road. Parking there avoids commuters getting stuck in any early morning traffic jam into town, and it is free. But you have to feel for the residents who loose their scenic view across the river, and parking for their visitors.
If you lucky enough to find a slot you can fit your car into. Suppose it depends which time / day you try.
It is also quite hazardous cycling past a relentless line of cars with an impatient driver behind and a road hog coming in the opposite direction.