I have a blocked downpipe which probably needs replacing

Not sure whether the problem is just with the pipe itself or whether there is a blockage below ground ( council surveyor thinks it may go into a soakaway)

While it is on my land it is actually my neighbours pipe ( it is a row of terraced houses down a hill each with a front garden and each house is slightly in front of the one next door) so they should pay but I just want an idea of the possible cost before I approach them.

Anyone either do such work or know someone who does?

Thanks7