Cover the bottom of the slow cooker pot with the carrots and fennel.
Prepare the chicken by rubbing it all over with 1 tsp oil and the garlic, then place the lemon, thyme and garlic inside the cavity. Season the outside of the chicken and place it on top of the veg in the slow cooker. If the chicken is too big for the lid to fit snugly, move the vegetables from underneath to the sides. Cover and cook on the high setting for 4 hours. When there are 1 hour 30 minutes remaining, add the leeks to the slow cooker.
Meanwhile, bring a large pan of water to the boil and add the potatoes. Cover with a lid and simmer for 18-20 minutes or until tender but still firm. Drain immediately, then toss with the remaining olive oil and parsley. Season with cracked black pepper.
Place the chicken on a platter or chopping board and carve, serving with the juices and vegetables from the slow cooker and the new potatoes.