Newcastle an East Midlands certainlly use their scales..
My guide would be as follows
Bike padded out in a securely taped up box with any riding gear, spd shoes, lube, tools, gaffer tape and your wash bag. make sure that it's no more than about 30kg. (airport kg are smaller than real kg)
Everything else in your hand luggage (dakine cabin roller is the biggest you can get on to all airlines no hassle). If you bike is pushing the 30kg, you can put pedals, innertubes and shock springs (where applicable) in your hand luggage. I've had mine up to 18kg before now.
Helmet in your hand. It's too important to go though as checked baggage.
Alternatively frame+forks and a few bits and bobs in 1 box or bag (20 airport kg.) This box is your "bike" Wheels and further gubbins in another package(12kg). This is your "case", on top of which you still have your hand luggage. This is easier to manage if you're not into hulking all 32 kg in 1 go.
Boxes are much lighter than bags and offer more protection IMHO.
No arguments with check in staff required, easy, as Easyjet ought to be.
Any more than that and you're taking too much.