Be aware that if Khan gets his way both Abbey Wood and XP will be within the ULEZ zone so if you are not compliant it will cost you £12.50 per day to enter the zone.
For XP the best route for you will be M1/M25( clockwise)/M11 towards London then A12 past the Olympic Park and through the Blackwall Tunnel onto the A205 South Circular clockwise turning off (south) somewhere near the Horniman Museum onto Sydenham Hill which will bring you out opposite the site gates.
You can get a No.3 bus on Crystal Palace Parade about 300yds from the site gate which terminates on Whitehall close to Horse Guards - takes about an hour and costs £1.75. Return bus stop is opposite.
You can go by train from XP but its quite a long walk to XP station especially if it is dark and you cannot walk through XP Park.
Abbey Wood is a nice site. Go M25 over Dartford Crossing* then onto A206 towards the city until you come to some lights with a right turn A2041 to Abbey Wood station. Turn right down the hill and take first left (tight turn) as you come out of the trees - the site entrance is on the left.
*Dartford Crossing is pre or post payment and uses ANPR and is chargeable 06h-22h seven days a week. You must pay on line or at any Payment Shop before midnight on the day after you used the crossing or open an account (on line) and use the crossing as you like so long as you have enough credit! Cost is £2.50 or £2 if you have an account. Caravans are free. If you open an account and don't use it for a long time (2 years?) they will refund your credit upon request.
Abbey Wood to London is from Abbey Wood station about 10-15 mins walk from the site down the hill on the main road. The main service is on the Elizabeth Line (a.k.a. Crossrail) of which AW is one of the eastern termini. There is also South Eastern Trains which will take you to London Bridge or Cannon Street.
Good luck, enjoy, and take <plenty> of money with you - card payment preferred.