You are missing something - the USA. The US market is the biggest by capital traded in the world. If the US goes up, we will follow. Say the US markets are at a certain level at 4:30pm when the London Stock Exchange ceases trading for the day, e.g. the Dow Jones Industrial Average, is 10,700. As New York is 5 hours behind London, the US markets keep trading until after 9pm. Suppose the Dow is driven up to 10,850 after London closes. It's highly likely that the FTSE100 will open at 8am next day significantly higher (actually about 150/2 = 75pts).
But if you're an IG customer, you can keep buying through the evening and through the night, but naturally, the price you will have to pay will rise, because IG aren't wanting to give anything away - they're like a retailer who just got a call from New York to say everyone's going to be buying tomorrow, so they're certainly not going to announce a cut-price sale.