Although I get the frustration, they definitely removed the old warp key for a reason - being able to warp everywhere at the touch of a button would make some quests ridiculously easy, and now that Potterworld has more of a questing system, the ability to warp with the old warp key would be too overpowered.
I think a lot of people are frustrated with this at first, and even when you're used to it and have a really good broom it gets frustrating sometimes, but as you get used to it it won't be as much of a problem.
Recently, Scarlett's been added in to help you navigate Hogsworth, and navigating the wilderness is incredibly easy as all you have to do is grab the co-ordinates from the map and go there.
As for reaching London, as Avi mentioned, the quickest way to reach London is fire dust or the vanishing cabinet. You can also use the train, if you'd like. I've forgotten the cabinet co-ords off of the top of my head, but if you ask in chat I'm sure somebody will know!
Also, I expect that somebody will already have made a post on this before - there WAS a similar one a while back that involved having 2 warp slots instead of 1, but that's not the exact same as what you are suggesting here.