Who is responsible for this repair?

[lalalonglegs]

I own a flat in a converted Victorian building. There are three other flats and we share the freehold. The owner of the ground floor flat built - with our permission - a large extension and I can see the flat roof that covers this is already pooling water and I am sure it will fail in the next few months (it was built less than a year ago). I am really reluctant to share the cost of repairing this as it is was his decision to choose these builders who are unlikely to have offered any guarantee. Could we argue that we are only collectively responsible for the original building and not any add-ons?

Depends on the repair/service charge clause of original freehold deed and whether this deed was altered formally when you agreed to the extension and if so, the terms of the new deed. It's bit difficult to provide advice on a forum as repairs for shared buildings is a complex area and its unclear to me whether you had any 'say' over the roof specification in the first instance.
Consider consulting your solicitor (assuming the consent to the ground floor tenant was dealt with by your solicitor), failing that, Any chartered general practise surveyor worth their salt could help you on this if you take a copy of your title to them plus all details of what's gone on and a few photos of the issue. You might consider asking the other building sharers if they are equally concerned, and agree to share costs before you proceed to take advice. Note also depending on the building contract for the extension, the ground floor owner may still be in their defects liability period and they may have no idea about the issues.

Thanks for posting. The agreement to allow the extension wsscall very informal and I'm guessing the workers he has used don't issue guarantees. I know the other owners are cross about it so I suppose we had better pay for a bit of sdvice to (hopefully) save us money further down the road.

If informal, then in equity, it would unreasonable for you to have to pay for maintaining more than the original building. Devil is in the detail of the orininal deed though so advice route may be best to settle your worries.