Ok, I'm not sure where you are coming from, it may be quicker or easier for you to get the bus or train? You should be able to park at Sidcup station for £5 for the day, there is also a Morrisons nearer the high Street (Jenner Close) which should be free, this would be about a 20 minute walk. There may be parking on or around Hurst Road in the residential streets but I'm not sure about the restrictions for this.
For Bexley Grammar, I'm not sure about the local roads, but I would be tempted to park in Danson park and walk through the park. Probably take 15 - 20 minutes but would be a pleasant walk & nice start to the day