Double Kitchen Sink - Always Backing Up

[LiviFri]

Help! Moved into place with double kitchen sink. Each sink comes with a plunger-like plug that's almost water-tight but not quite. Whenever a significant amount of water is emptied into one sink (say medium pasta pot), water spouts up the other sink hole. This happens even when one of the sinks is plugged. Especially bad when the washing machine/dishwasher operate, so hard to wash up or cook while either of these appliance operate.

Never lived with a double sink before, so it may just be possible that I'm using it incorrectly. However this doesn't make sense.

Have tried using one sink plugged with soapy water and one sink as a draining sink, but this doesn't help much. Water still backs up in the free sinkhole and even a bit in the plugged sinkhole, which contaminates the soapy soaking water.

Is there a trick I am missing? Bathroom, shower and toilet all OK. I have tried various home remedies for unblocking any gunk that may be in the kitchen drains, but have yet to try chemicals like Mr Muscle. I'm allergic to chemicals and I worry the chemicals might back up if this doesn't succeed...

What make is the sink? Sounds to me as they the waste pipework might not be right. Can you post a photo of the pipework under the sink?

There seems to be no visible label of the make/company. Here are two pictures above and below the sink so you can see the structure. The sticker you see in the under-sink picture have random number on it and is part faded. But I don't think this had any wording/logo on it.

is that a kink on the left hand pipe that would stop it draining properly? Therefore the water has nowhere else to go and will back up?
But wtfdik?

Honestly innagazing it's like a forest down there :(

Here's a close-up of the kink (if this is what you meant). Don't know if this is normal. Washing machine, dishwasher and both sinks all drain down to this spot so is it possible this is meant to slow down the flow from the sinks?

Does the sink drain slowly too?

Yes, both sinks drain slowly.