Tricky gutter repair

I have a tricky repair job I’ve been asked to do.  The builders bodged the roof and the gutter is leaking at the corner.  I thought a new downpipe Is the best solution, but still not guaranteed.

There is a drain in the neighbours garden, though the exit is sealed.  I’m sure it leads into the main waste pipe though.  
 

any ideas? Should I fit the pipe and cut a hole into the drain? 

Unclepigg said:

Should I fit the pipe and cut a hole into the drain? 

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That looks like a drain that serves a few properties, if it is I'm fairly certain it belongs to the Water Company in the area. I'd get in touch with them first if I were you. Can you not just dig a deep hole and make a soakaway drain.

I couldn’t be bothered with all the faff it certainly isn’t going to give me my hourly rate , so I would suggest they get a builder in end of . 

That's a job I usually get. Can you not fit a new downpipe right into the grey connection below? You might need to fit a running outlet on the gutter and two 112.5 degree bends at top which takes you into the new downpipe.

Thanks guys.  Someone also mentioned a hopper outlet flush at the top.  I’ve never fitted one of these. Any thoughts ? 

Unclepigg said:

Thanks guys.  Someone also mentioned a hopper outlet flush at the top.  I’ve never fitted one of these. Any thoughts ? 

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Between gutter at top you would need to fit a running outlet. Then a tiny piece of pipe, 112 degree bend, small piece of pipe, 112 degree bend into downpipe and a socket for two pipes at bottom to fit together.