If you want a cheap flight from Birmingham to Moscow, you've got zero airlines to choose from.
Moscow Vnukovo Airport is just one of the airports in Moscow. If you're not set on a specific airport, try changing your search from Moscow Vnukovo Airport to Moscow to see a broader range of flights – they might be cheaper.
During this peak season, accommodation prices often increase too, so it's best to book early. Or you could keep your fingers crossed and hold out for a last-minute deal.