From experience with developers, once you have purchased the property, they won’t even spend 4 pence in putting it right and they will either ignore what they are told to do, ignore your correspondence, spend thousands of pounds arguing as to why something shouldn’t be done or they have no liability. Perhaps I’m being cynical but that’s 25 years experience of newbuild developers. Incidentally, car dealers, especially new car dealers and manufacturers on exactly the same.
By all means try a strongly worded letter from your solicitor and if it comes from all neighbours, so much the better.
However you cannot beat the developer with the stick and if they resolutely refuse to do what you are reasonably asking for, then you are faced with taking them to court.
I think you have a substantial claim here for loss of use/amenity respect of the waterlogged garden.
You have a claim under the provisions of the Consumer Rights Act 2015 because the goods (the house) are not of satisfactory quality because of a whole variety of reasons including the downpipes and the drain.
If you are making a court application you can make an application for specific performance which is a court order to compel them to do the work but it would be more common for the court judge to award a chunk of money in order for you to get the work done yourself.
You talk about driveways in your “preferred finish”. You would obviously only be able to have them redone in the finish as they would have been done when you purchased the property.
Can I clarify anything else for you?