Jugs, based on your post and the PM I just received, I'm getting a very strong feeling that Easyjet might be a far better option.
You say you've got a CPL but you're not able to figure out how much time and money you need to expect for the crossing. You've got an IR but you don't know how to plan an airways flight, apparently. And you've got a fixed date in mind on which lousy weather (including icing at any meaningful altitude) is a real possibility.
Build your experience slowly. Do a Channel crossing when there's no pressure to be on the other side at a specific date or time, so you can wait for reasonable weather. Expand your experience from there. But the plan you seem to be creating now has a very strong possibility of ending in tears. If not worse.