The water drains increasingly slowly from bath tub and sink

Crystallization of fat and oil blocking the drain if it's on the same pipe as kitchen in which case put a few times very hot water down the drain to make the fat melting. If it's not on the same drain than probably a ball of hair caught somewhere down the line, plunger is still the best way to try to get it moved first before go with drain cleaning coil or rod. Adding baking soda and vinegar to the water makes the process more successful, or leave bleach in the drain overnight in case of hair blockage, just make sure you clear bleach off the metal parts.

WARNING:-First and foremost, wear gloves,goggles,mask, etc.. when messing around with drains. A foreign body in your eye,mouth or on your skin could cause disease. This sounds as if your main drain or soil pipe is either blocked or damaged. If you can lift a manhole yourself and can see that it's not full or blocked & water runs freely, it will narrow the problem down to between there and the main soil & vent pipe. If you live in an old property a drain could have collapsed. Have you or anyone in the immediate vicinity had building work done, where something could have got washed or accidentally dropped down the drain ? Options are to get a drain specialist in who has camera equipment, this could be costly to start with & then there's remedying the problem but at least you'd have had a visual check on the condition of your drains. Alternatively get a plumber or builder to take a look as they will understand the possibilities & be able to narrow it down or remedy the problem. It could be that rodding a section of pipework could sort the issue. Some blockages are too much for drain unblocker fluid. Toilet wipes are known for causing problems as they line the pipework when they get snagged or don't flush properly. Nappies are the worst offending item, they act as a plug & swell up, but I assume that's not the case here. Above all, consider health & safety at all times & in all ways. Good luck