The peak season in the UK lasts from July to August. For a tourist, the best time to go to the country and particularly to London is between April and June. You will be able to enjoy pleasant weather and attractive prices for business class flights because they are cheaper than during the peak season.
Another good option is going to the UK from October to December. Since it is considered to be the low season, you can purchase business class or first class flights really cheap. The cheapest month is November. You can still book a cheap flight in the high season, but you should do this beforehand, let’s say, two months before your departure date.