Youre either playing the slav or the london. Youre not playing the slav while your opponent plays the london... youre playing c6 after a few opening moves, which is a common move against london setups. Its not the greatest "anti london" , but it is a fine move usually followed up by qb6.
c5 is better imo.
If you play the Slav and the Caro you can play 1...c6 to 1. d4 and then play the line with ...Nf6 and ...Qb6 against the London. The idea is to go on to play ...d6, grab their dark squared bishop with ...Nh5 when possible, then fianchetto on g7 and strike against the center with ...e5 or ...c5.
Here is a game I played in this line. It's not a great game from me (when flicking back through it I was particularly like "bro what are you doing" at 11...dxe5 instead of ...Nxe5) but it illustrates the ideas of the line quite well.