All these symptoms are typical of a blocked sewer. You need to find all the access places on your property and probably even next door and discover exactly what is blocked. It may not even be on your property!
Had a similar problem with drains at my old place. After checking with the neighbours I discovered they were also having issues so I called out the water board. Turns out there was a blockage in the sewer a couple of hundred yards up the street that was causing the problem.
If your neighbours are also having issues then call out the water board as it shouldn't cost you anything. If its only you then it could be a blockage in the main drain pipe connecting your property to the main drain/sewer. If that's the case then its you that has to pay for it to be cleared.
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