Our robins are like your wrens - they can get very tame and they certainly use humans as a mechanism for getting food. They will perch nearby as you dig the garden so they can grab any worms they see and when I say "nearby" I mean they'll watch from the fence or even perch on the bit of the fork/spade you haven't got your foot on. Mine sit on the buddleia or viburnum waiting for me to add suet bits to the food - they'll eat the rest but if I forget the suet their displeasure is quite apparent.
The picture below is one of them on the buddleia yesterday. No way of knowing if this is the male or female - they both look the same. About 5-6 inches long - same size as your blue wren. Our wrens are smaller, about 3-4 inches; there are wrens in the garden but they don't stop still long enough to photograph. They're noisy little birds though - the RSPB has an audio of one here
. When the robins and wrens all sing in the morning it can be very loud!