Unfortunately i have to go put my bag in airport How mutch � do you think i will waste in the follow route?

There are a number of Left Luggage desks in London Stations. Why not leave your luggage at one of the Stations you are going to? Waterloo and Liverpool Street both have left luggage (details on the link below). It will cost you �8, but save you so much travel time and allow you to do a bit more in the time you have left in the UK. Both are open until nearly midnight (check if you decide to do this), so you should have a good few hours before you have to pick it up.