Oil a 950g loaf tin (ours measured 19 x 9cm across the base) and line with a strip of baking parchment, leaving a little hanging over the edges – this will help you lift the cake out later. Heat the oven to 170C/150C fan/gas 3.
Put the butter and caster sugar in a large bowl, or stand mixer. Beat together using an electric whisk or the mixer until pale and fluffy – this will take a few minutes.
Gradually add the egg, a little at a time, beating well between each addition until the mixture is smooth. Add a tablespoon or two of the flour if it’s starting to curdle.
Add the remaining flour, the milk and vanilla, and mix until there are no visible streaks of flour. Scrape into the prepared tin, then use a spatula to evenly spread it and smooth the surface. Bake on the middle shelf of the oven for 50 mins-1 hr, or until a skewer inserted into the middle comes out clean. If any wet cake mixture clings to the skewer, bake for 5 mins more, then check again. Leave to cool in the tin for 10 mins, then carefully transfer to a wire rack and leave to cool completely.
Chop four of the strawberries into small pieces and mix with 1 tsp of the icing sugar. Set aside. Halve or quarter some of the remaining strawberries and leave the rest whole. Mix the remaining icing sugar with 2 tsp of the jam and all the lemon juice to make a thick icing – it should be thick enough to drizzle down the sides of the cake. Pour the cream into a bowl and whisk until it’s just holding its shape – be careful not to overwhisk, as it will continue to thicken as you pipe it. Transfer the cream to a piping bag fitted with a fine star nozzle.
Slice the cake in half lengthways through the middle using a sharp serrated knife. Spread a little of the remaining jam over the base layer. Pipe half the whipped cream over in a zig-zag pattern and top with the chopped strawberries and any syrupy juice from the bowl. Sandwich with the top of the cake. Pipe the remaining whipped cream over in the same way, then arrange the halved, quartered and whole strawberries on top. Drizzle over the icing to finish. Best served the same day, but will keep covered in the fridge for up to three days.