What sort of tradesman? outside drain issue.

[QueenOfAccidentalDeathStares]

The outside rain takes water from the kitchen plus one on the rain gutters. It is sat with concrete around it in a brick patio.

After spending a nice 10 minutes unblocking the outside drain, I have discovered that the concrete around the drain has large cracks in it which have gotten a lot worse this winter. In addition, the brick patio has sunken slightly around the drain so probably needs relevelling.

Is this just a builder job? or a patio-repairman job? I mean, the drain itself is ok, but the concrete/patio around it is knackered.

A builder who understands drains. It might need a reconstruction. Does your roof water have to go into the drain? Can you recycle it?

Don't see why it has to be a man, but I'd say get a drain company, or a general builder.
Basically you're going to have to dig until the pipes underneath are exposed, and replace with plastic, then back fill and compact then reinstate the paving

I'd start with a company that deals with drain installation. They should be able to recommend someone who can do the job and also understands drains who they work with normally.