I think this is a strange way to think about costs for a child, but you are spending a lot more than we do on activities, toys and clothing.
Most people would count food and petrol costs just into their normal household spending. Presumably when you take him to nursery, you then drive to work? (Unless you work from home I suppose).
We did quite often buy those baby ready meals when DC was around 1yo but as the youngest got older relied on them less and less. I can't remember when I last bought one and he was 2 in the summer. We do have some convenience foods like chicken nuggets, oven chips, frozen pizza or the ready made pizza base + sauce kits which we put our own toppings on, that they like. We were buying pasta + sauce kits (where you get the dry pasta with powder and adding water to a pan rehydrates the sauce and cooks the pasta) but honestly it works out faster, cheaper and easier to just make pesto pasta, or cook pasta, add cheap tomato jar sauce, tinned sweetcorn and some chopped ham, or cooked sausage, or just grated cheese.
We don't batch cook really but sometimes for example I'll make a portion of spaghetti bolognese in the evening for me and DH and save some portions of this to put in the fridge for DC the next day, or freezer to keep spare. This also works with chilli, curry, soups, stews etc (whatever the DC like). Pasta bake can be done for adults in evening and reheated the next day for DC.
Jacket potatoes done in the microwave are a hit. They don't eat the skin whether it's crisped up or not, so no point crisping it. Sometimes they also just eat something like beans on toast, or even porridge. Oh, tinned ravioli is probably the closest thing to the baby ready meals that I buy now.
In terms of activities, we would not do expensive activities like that twice a week, that is a lot - we would probably do them once or twice a month depending on whether we have cash to spare. If you don't have time to cook after work then when are you even doing these things? Do you mean you do a paid activity on every weekend day? We would typically do free or low cost activities at weekends, mostly - walk in local wood, try out different parks, bike ride (yes the bike + helmet is an upfront cost), feed ducks, visit friends/family, go to library, go to local free attraction/consider a yearly pass to attractions we would like to go to more often (or make lots of short visits rather than feeling we have to "get the value" out of the entrance ticket).
Toys are not bought every week or anything close. Yes they do need different activities for development but you don't need tons of "stuff". Try using the things you have in different ways. IME they also get overwhelmed being faced with loads of toys and play better when there is less choice offered.
I do actually track clothing spending 
This is on average about £30 monthly, that is for two young children so there are some hand me downs. But again they do not need new clothes every week. I probably do buy them at least one thing a month. (I just looked back and there was only one month I bought nothing). Actually you will probably find clothing spending slows down - from 0-12 months they go through about 8 clothing sizes, whereas there are 2 between 12-24 months and after 2 it's roughly 1 size per year. So I think with your first child you are buying clothes non stop the first year and then this does settle down.
£25 per week is low if you're including things like food and nappies but £400 a month is a lot IMO.