Commercial property is leaking water through the roof

Hi all! I was wondering if you guys could help me with a problem.

UK based, Greater London

So I own a business on a high street and currently rent a commercial property from a landlord. The property has two flats above the shop, with one of the flats having an outdoor terrace space directly above the back of the shop. This outdoor terrace space is the main cause of the leakages as the surface of it is concave, and rain water tends to sit without draining away. The length of the lease is 10 years, and we have currently been there for 5 so far. During this time, the roof has continued to leak water into the property and has done so since we have been here. We have a decorative sculpture on the ceiling and at one point it had gotten so bad, half of the sculpture had fallen down onto the floor over night with water pouring in through all the gaps it had created. We are glad this had happened over night, as if it were to happen during our opening hours, some one may have been seriously injured.

The landlord has sent multiple builders/roofers around during the course of our tenancy to try and fix the issue, but the issue is never fixed. There has been drain gutters installed on the edge of the terrace area but they do very little to drain the water away as the water sits in the middle of the terrace. One of the roofers that was sent round to fix it has told me that the landlord has built an extension on one of the flats upstairs on top of our roof, and to remedy the issue permanently, the extension needs to be demolished so that the whole roof can be replaced. Obviously, the landlord doesn't want to do this as it would be very costly for him and refuses to accept this as fact.

After a night of heavy rain, I am greeted in the morning with a pool of water on the shop floor. I have taken pictures and documented all this each time it happens, with emails being sent to the landlord with the pictures attached. Its been 5 years since we've been here and I'm still having to deal with this every time it rains heavily over night.

Do I have solid grounds to be able to win a court case against him? And what would be the best way to approach this?

Thanks for your patience in reading this.