Honestly, unless you start wandering the streets dressed in a onesie, it's hard to imagine that you'll look out of place. I frequently go into Town wearing jeans, T-shirt, fleece, anorak (or similar) and sneakers. I might dress up for the theatre (ie wear a dress and leggings) if I felt like it, but would not be at all surprised to sit next to a person in jeans and T-shirt, etc. It really doesn't matter, unless you want to go somewhere (probably a night club or a restaurant in a top-notch hotel) where there might be some requirement for smartness - and there'll be some indication of that.
I thought your post was going to be along the lines of 'what will the weather be like?' to which the answer is, nobody really knows. We could have glorious spring sunshine, permitting semi-hardy folk to be in the parks in T-shirts. We could be knee-deep in snow (although in London that is *very* unlikely). Most likely it'll be cool with quite a bit of rain in prospect, and a reasonable possibility that it will be cold and windy. Bring layers, and have hat and gloves at the ready. Aside from that, dress at the level of smartness/casualness/fashionability/comfort that you feel most comfortable in. You'll be fine.