I don't think you get more Avios when booking with Avis BA as opposed to booking direct and entering your EC number, but I'm happy to stand corrected.

However, if you book direct you can get ~9% cashback through TCB, which on a £200 booking works out at 4400 Avios (6500 when a conversion bonus is on) when converting via Tesco CC. So, if you can get a CC conversion bonus, you'll earn 10x as many Avios that way as you would booking through Avis BA.