We did baby classes - it was how we met people with similar-aged babies. There's a few free ones near us but they tend to be less community-driven, people don't tend to come to them regularly. We signed up for a couple of different classes to give us things to do each day, especially when DH went back to work. They were usually £50 a term, or so.
Swimming here is £68 a month, but you have to commit to three months at a time.
You probably won't need a travel cot. They get bashed around a lot in the hold, as do car seats, even boxed. If you are taking a car seat, you'll want a "travel" one that you don't use at home.
You may well need a new car seat in the first year, depending how big baby is. Our infant carrier lasted until 14 months. You'll probably want an ERF seat after that which can be expensive, but lasts a lot longer than the spin-style ones.
Food - we only really bought snacks, and then extra fruit and vegetables to cook home-made snacks. We did BLW so he had what we had. He still does, he's a great eater. We don't cook separately for him. We didn't need purees or anything.
We didn't use nappy bags, or a nappy bin, just put the nappies in the bin and emptied it often. We used Pampers, which meant we didn't have too much extra washing, as they didn't leak for us. They cost £6-ish for 50 when he was tiny, and now around £14 a pack? He's been toilet trained other than night times for a couple of months now. There tends to be offers, if you can be flexible in where you go to buy them and when you buy them.
Have you checked the childcare cost? It's very variable. A 1-year-old doing 2 days a week with the 15 hours funding would cost £380 where I am.
We didn't use a walker, we had a Jumperoo but it's far from essential as they aren't supposed to go in for more than 5 minutes at a time and 3 times a day. We got ours from Marketplace. It's held it's value, they're selling for more than we bought ours for now. There's always cheaper designs, too.
Books we buy pretty often, but usually from discounted shops, and that's not an essential.