Concentrate upon being kind to yourself, not focusing upon what you feel is bad or shouldn't be done.
The idea of taking the baby out for a ten minute walk every day is a really good one - if the weather is hot where you are, taking advantage of early wakenings means you can start the day with some fresh air and daylight before it gets too hot. Put on some comfortable clothes, wear supportive trainers/running shoes (foot care - making your feet aren't dropping in as you walk - is really important for making any physical activity more enjoyable). Then go home and have something to eat that makes you feel good - things like fruit, yoghurt, grains, fruit and cheese, maybe bacon on avocado toast, something that isn't just carbohydrate plus refined sugar, looks pretty, tastes good and adds some extra fluid and nutrition, compared to a standard British breakfast.
Have chilled water in the fridge and make a point of drinking, even if it's just a small glass, frequently - sometimes, dehydration can make people feel a bit disorientated or anxious and if you're feeling up and down, it's a way of retraining any instant reaction to emotions by eating. You could add slices of lemon and lime to the jug if you want a different flavour (or more strawberries, for example).
If cooking meals from scratch is too much for you at the moment, so you're going for takeaways, ready meals or snacks, are there any other things that you could have in the cupboard and fridge that are easier? If you like lots of vegetables, perhaps either jars or packs of things from supermarkets that can go on a plate/in a bowl with cherry tomatoes, prepacked mini cheese, cucumber, celery and carrot sticks, dips, etc, might work for you - because you're eating more vegetables that way. It's a lot easier to open a few jars and assemble stuff than it is to cook an entire meal.
If you're feeling anxious, rather than pace around feeling trapped, you can go out again for another ten minutes. Anxiety is the body's fight or flight response - ten minutes of activity, especially if it means taking yourself away from the place where you felt that feeling, tells your body that you've acted on the perceived threat, so it responds by relaxing.
There's nothing wrong with taking yourself off for a shower or bath with the baby either with their father/another relative, in with you (so it's a nice play activity for them) or safely beside you in the bathroom.
Just from doing things that make you feel better, you might find it easier without actually 'punishing' or restricting eating - you're reframing it into doing nice things for yourself. And then you might feel ready to make further changes/improvements in how you care for You.