What kind of tradesperson do I get for this job?

[schroeder]

I have a brick built shed with a broken door frame also some rubble to shift (just a couple of barrows worth I imagine)

Is this a job for a chippy? and a man with van. or maybe just an odd job person?

Either; way how much would you expect it to cost?

If the door frame just has a simple upright or horizontal that needs replacing, I would use a handyman. If it is more complicated than that and you need a carpenter/joiner, he is not going to shift your rubble for you.

How much it costs depends on local labour rates and how much material is needed. As it sounds (to me) a small job, I imagine they won't be falling over themselves to do it and it could end up costing more than it needs to, iyswim. Honestly, if it's just a question of jemmying a piece of timber off and banging a couple of nails into another one, why not have a go yourself?

Well I am tempted, but I think I might have to drill new holes and I don't think I can get the drill to reach.

Also I don't want to make a complete hash of it and make myself a sideshow for my neighbours.

But yes you're right I can't see anyone being desperate to do it.