never rains but it pours

The lovely weather this weekend highlighted a previously unobserved feature of our basement flat, a leak.
Our kitchen is under the pathway leading to the ground floor front door of the flats above (so long and thin, or galley style as the estate agents would have it). It has been tanked on the end wall and side wall and pre-existing plasterboard left in place on the ceiling and other wall.
So clearly there is a problem and it is now all buried. It seems most likely to be coming through the roof. We did check the water-proofing on the ceiling, but it was Summer and so hard to test thoroughly.
The water is coming through very slowly, just about running down to the floor in one or two places.
So the question: access to the ceiling is a nightmare. Is there anything we can do on the outside to improve the waterproofing? The pathway is asphalt - is there anything you can paint onto asphalt to make it more water resistant?
Any thoughts much appreciated
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
Add image file
Upload is a website for homeowners and building and maintenance pros. It is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.