Not a proper pet but thinks he is...

Is it defending its territory against its own reflection?

I really don't think so - that was my first thought but it seems very happy & sits there singing his ( I don't know if it is male or not) head off all day. He eats the food & he is just always there. He looks into the room with his head cocked & doesn't mind if I get very close to the window. He doesn't even seem fazed by cats on the window sill now.

It's very odd.

I have been walking in woodland this afternoon and noticed that the robins were singing their hearts out, but surely it is too early to be trying to attract mates. I wonder what is going on.

I did a Google search, which did not really explain the robin's behaviour, but both sexes sing most of the year round except during the moult, which will have just finished.
www.garden-birds.co.uk/birds/robin.htm

He's still here & behaving just the same except he now waits in the hedge every morning singing away until I fill up his food- usually he starts at daybreak so he has to wait a while. A bluetit has started feeding too but he gets chased away if Bob the Rob sees him. I think he will be with us for the winter now. He has stopped flying into the window which is a relief- he just sits in the hedge or on the feeder.
I think he is just a very clever little bird who has found a way of getting his own food source. I am even looking at robin's nesting boxes now so maybe we will have a family next year.
The cats have decided they can't win & mostly ignore him now.
We are really quite fond of him now he is sort of part of the family looking in the window all day.

With patience, it is possible to get robins hand tame.

Some birds mate all year round. Perhaps robins do. The singing would be to attract a mate, and the reflection fighting would be defending its territory.

We had one a few weeks back at the holiday cottage we were staying in. Doing just the same thing.

can have four broods a year!

This thread is a decade old but I found it when googling details about Robins singing up close to you and thought I’d see if anyone else has found the same.
Our usual Robin hasn’t got a mate this year. He takes mealworms from our hand but eats them straight away, so hasn’t got a family to feed. If we’re in the garden, even after he’s had mealworms, he settles close and sings fluffed up and moving his head from side to side almost as if he’s singing to a mate. Maybe he’s just a lonely old frustrated Robin but it would be good to know if anyone else has had this experience.

We have a family of robins who are always in the garden singing their heads off,we love it.

They are incredibly territorial birds.
I imagine the singing is them proudly marking their stamping ground.

Please can I swap your robin for this?? This crow and others come several times a day to most of my upstairs windows to attack their own reflections.