If the manhole is inside the boundary of your property and is not shared with another household, it is your (or your landlord’s) responsibility. The manhole cover is usually an access point for a drain and not the main sewer.
If your property was built before 1937, the council is responsible for maintaining the drains, but they can claim the cost of any repairs from you.
If your property was built after 1937, it is your responsibility or collective responsibility to clean and maintain the drainage. Your local council can help you to find out whose responsibility it is.