ha.. very close to me. I'm on the Davis Estate, Southlands Ave behind the Crescent.
So yes the A21 would be the best and quickest route.
So what I suggest is, Sevenoaks Road, Right at the roundabout by the bus garage. (bit of a climb here). Then the A21, up to Locksbottom (another little drag), then down hill into Bromley.
Kentish Way, then right to go down the (very fast) Bromley Hill (you can get to 40mph if you push

) ...keep going, past Downham, Catford (being careful of cars wanting to turn left into Canadian Avenue) towards Lewisham, over the large roundabout, cross the A21 and that will take you straight into Cutty Sark.
Click
this link for a mapped route
Points to note for the return.
As I said previous. It's a bit of a drag the return as not only do you have to climb Bromley Hill, you will also have to climb up to Locksbottom. But it does leave you with a nice and fast last stretch to home.
In both the mornings and evenings Bromley is probably the most congested part of the route.
At Catford/Rushey Green. You have the option of either going round the one way systems or through the bus lane. It's half dozen of one etc as to which one is fastest. Though the Bus lane is the safest.
Climbing Bromley Hill, it can seem intimidating as the road has islands, so be careful not to let yourself be squeezed by cars, buses or lorries. Once in Bromley, be a bit mindful of Kentish Way, it's a nice bit of road to cycle but cars do treat it like a race track.
Personally, I think it's a perfect commute distance. 12 miles to Greenwich. Once you are up to speed you will be able to do it in 45 minutes, but a bit longer on the way back.
ps forget the facemask. You don't wear one when walking the streets do you? They just get all hot and sweaty and yucky...and don't really work.