It is very difficult to comment sensibly without many more facts, but I am quite involved in that area, not as a lawyer or managing agent.
I think you will find it hard to pin liability on the managing agent, especially in the middle of a pandemic. Assuming the leak originated in the common parts drainage then it may well for example have been caused by some idiot in another flat flushing eg wet wipes, in which case there may be an argument for them being liable. However your lease will probably require insurance for the building as a whole, which may well cover the costs.
If you really want to talk to a lawyer then I recommend Alexandra Adam at Gregsons in Wimbledon - she's very sensible, will tell you honestly if you don't have a good case, but will do fine Rottweiler impressions if you do and you instruct her. Her phone number is 020 8946 1173. Good luck.