I'm probably ignorant of how your washing machine waste water line is plumbed into the household waste as compared to here in the U.S., but it sounds to me like there are a couple of possibilites.
Firstly, any cleaning agents you put down the sink will only affect the gooseneck "p-trap" under the kitchen sink. (the "S" shaped device under the sink.
When the washing machine discharges waste water, it causes a suction and pulls the required water out of the p-trap and gases bubble back up through it. The suction is normally avoided by the vent pipe you see coming through the roof of the house.
First, the line from the sink to the outside should be "snaked" or rodded (not sure of th evernacular in the U.K.)
The second, would be to make sure the vent line isn't blocked. If you can (safely) you can inspect it on top of the roof. It may not have a rain diverter on it and it's not uncommon for birds or other debris to fall into it blocking the air return. It would be far better to have a professional "snake" it out as well...
Best of luck!