Weekends no problem.
Weekdays (and this may seem surprising considering the number of spaces), yes there can be a problem.
I'm a leisure traveller and have to pay for the parking myself so would not dream of paying £15.70, yet there are enough business travellers and season tickets regulars to mainly fill the car park up.
If you get there around 10:40 to 10:45 just in time for the reduced rate intending to catch the 11:08 to Waterloo, you should be fine although you will be at the top of the multi-storey or at the far end of the ground park.
If you arrive there much later you may find all the spaces filled, as I did once. After about 14:30 you will be fine as people start returning.
My experience (not scientific) is that Tues, Wed and Thur are the worst days when it is liable to be full.
Friday you are probably fine and Mon (perhaps strangely) also seems to be not quite so busy.
On main school holidays and half term weeks there is also a noticable drop off so you should be fine on any day then.
Plan B if you do get stuck --- drive to Eastleigh and park in one of the municipal car parks and catch the train from there. The 11:!2 will get you into Waterloo about 12:35 if you can't get on the 11:08 from Parkway. I can't remember the parking cost but it remains quite high not down to the £6 off-peak rate at Parkway.
I hope this helps.
