The installation and maintenance of adequate foul water drainage systems at your property is the landlords responsibility.
There is however a responsibility for the tenant not to cause a blockage or damage to the system for example by releasing inappropriate items such as wet wipes or nappies, oil or grease down a drain. If a blockage does occur you should contact the landlord in the first instance. If the landlord is slow to react or is taking no action then contact the Local Authority for advice.
If the blockage or leak is causing a problem to other people the Local Authority may receive complaints form elsewhere and may investigate the issue and can take remedial action if necessary.