I actually bought a new coat with three zippered pockets so I could store more stuff in them safely when I go through LHR security. It also has a liner that comes out and a hood that detaches so works from about -10C (with hood and liner) to over 20C as a raincoat.

Once I'm through security, I pull out a cloth bag and put my coat into it and anything else I don't need at my seat on the plane. That goes into the overhead bin and my carry-on bag at my feet. Security only cares if your stuff will fit into one bag when you are in the lineup. Once you are through, they don't care how many bags you put things in.