You have 2 hands. One is on the pram, and the other is holding an adolescent dog who has spotted a hedge. This used to be your dog's walk, and it is now a school-run leg with a deadline.
Decide what this walk is for
A walk you have to finish by 8:50am is transport. Training needs a walk you are allowed to stop, shorten or abandon, and this is not that walk. So the standard drops to 1 thing: your dog does not get to spend 15 minutes practising dragging you toward every hedge.
Manage the pram walk this week
Shorten it. 10 minutes of steady walking beats 25 minutes of hauling, and the leftover energy has better outlets at home.
Use a well-fitted front-attach harness, so a lunge turns your dog rather than pulling the buggy sideways.
Keep your dog on the outside of the pram, away from the kerb, and always on the same side.
Carry food in the hand nearest your dog, and pay them every 3 or 4 steps for walking level with the wheels.
Walk with a second adult for the first 2 weeks where you can, so each person has 1 job.
Train loose lead somewhere else
Split the walks. The pram trip is transport, and a separate 15 minute dog-only walk is where the lead work happens.
Pick a quiet stretch with no deadline, 10 minutes, 3 or 4 times a week.
Pay generously while the lead is slack, and stand still rather than pulling back when it tightens.
Add the pram back in only once a quiet street is easy, and start at 5 minutes.
Behaviour change is built from management plus reinforcement together. The harness and the shorter route are the management, and the food you hand out is the reinforcement. Reward-based methods are what the veterinary behaviour guidance recommends, and a busy street is no reason to abandon them.
Safety note
Never tie or clip the lead to the pram. A dog who lunges can pull a buggy over or drag it toward a road. Keep the lead in your hand, and end the walk if you cannot hold both safely. If your dog lunges at people, dogs or traffic, get help now from your veterinarian and a qualified behaviour professional.
Today's version, in one line: put the front-attach harness on, cut tomorrow's pram walk to 10 minutes, and pay every 3 steps.