Hang on....its losing water yes.
How can you tell its speed dependant?...especially given that you have to go from a standing start, back to a stop.
If it has already overheated, my money's on head gasket. When the rad on my 899cc went its water consumption was circa 5L in 20miles. The HG went the week after (taking the 'stat with) and water consumption reached 5L per 10miles @ 70mph.
Once it overheats, probability is the cylinder head warps just enough to retain a vague seal (the engine will run, probably very rough), and will dump coolant into the cylinders - so thats probably where its going.
Check the oil - if it looks like cappucino in the sump, or has creamy bits in it at the top - its got water in it, that means the HG has probably blown.
Oh, and check the system is bled correctly, you could have an airlock.
And I'll second the motion about checking the fan.