Firstly, Good luck ;)
I used to be a member at Westerham and it's not a bad course to have picked, while as a high handicapper it looks terrifying with trees everywhere, when you look at it objectively at a slightly lower handicap it is very short, so easy to navigate without using the longer clubs. So you will need to work on your irons being very accurate. I only used to take the driver on the par 5's and the 18th from the winter tees when I was playing there, and at mid to high handicap have broken 80 from the Yellow tees.
As I am still on their mailing list I saw your first round and you tube videos and without sounding too downbeat on your chances I think you are going to be hard pushed. When I first took up golf 3 years ago I flew to 28 handicap and then hardly stopped for breath as I got to 18, then boom I hit the buffer than requires a mixture of more tuition, more practice and more course time, all which require that most precious of commodities..time. I went to 18 in a year and in two more years have only dropped to a 14.
You may hit a few pars and think you are nearly there but to get that level par consistency is another ballgame. The difference between 20 handicap and hitting a scratch round (I'd guess being at least a 10 handicap to make that likely) whilst 'only' 10 shots is worlds apart.
I would love to eat humble pie though and will watch your progress.