vinegar will only get rid od limescale, which is not your preoblem.
It's usually a resident sludge of soap and fabsoft on which bacteria live.
Cause is usually cool washes (which don't dissolve soap well) and excessive use of powder and fabsoft.
Have you got some white cotton towels?
Buy a bag or two of Wasahing Soda Cystals (on the laundry shelf of your supermarket).
Put half a cup in the powder drawer
Put your white cotton towels and flannels in, a full load if you can because some machines reduce the amount of water if they sense a small load.
NO POWDER, NO FABSOFT
Put it on hottest wash.
If it foams up (it will) that's the old soap dissolving. Vinegar and bleach do not dissolve soap residue, but soda crystals do.
Do it again until it stops foaming.
The reason for choosing white cotton towels is that they won't fade (but they might go whiter), they will withstand the heat, and they will still fit you if they shrink.
In your future washes, reduce the amount of soap to min, and add the same amount of soda crystals. They soften the water, improve the action of the powder and whiten cottons, and dissolve the soap better. Don't add fabsoft, one of the reason towels go hard is an accumulation of soap deposits, and a reason they go grey is an accumulation of wax from the fabsoft.
You will be amazed at how many foamy washes you can get from the resident soap before you need to add powder again.
www.tesco.com/groceries/en-GB/products/285047163
www.sainsburys.co.uk/shop/gb/groceries/dri-pak-soda-crystals--fine-1kg
You can also use them to clean drains, plugholes and ovrtflows. Avoid contact with aluminium, which will go white or dull.