What would cause the water in the bowl to leak down to a little water left in bowl after flushing?

Look inside the tank under the lid, it sounds like the flapper that lets the water into the bowl is getting hung up on something when you flush. It could be the flushing lever. This would cause the flapper to stay open letting water to just pour into the open sewer line. It should be a simple fix. Just see what is binding the flapper & make an adjustment.

replace the flushing controls or install a new cistern

The bowl is cracked and is leaking down the drain. You will have to replace it. It may have cracked if the bowl hold-down bolts were overtightened, or the bowl was not able to sit flush (pardon the pun) on the floor. If the bowl rocks when it is first installed, instead of tightening the hold-down bolts, use a couple of tapered shims under the edge of it, then caulk to fill the gap and hide the shims.
Good luck.

Sorry for problem with new toilet.
You say water is leaking out of the bowl?

Toilets have 2 parts:
1) Tank: where water is stored for the flush and is sealed with a flapper.
2) Bowl: where water flushes down.

a) If tank is leaking water, then flapper is suspect. Replace flapper and see if that works.
Lift up flapper and run finger around rim to see if there is a rough spot that would indicate flush valve is defective, and needs replacement.
See typical flush valve

b) If bowl is leaking, that is very unusual and would indicate a crack in the porcelain.

If installer sold you the toilet, it is his responsibility to make good on product.
All products are guarantee against workmanship flaws.

There is a crack in the trap of the toilet.

Hello. Your toilet is leaking through the flush valve. This is a serious issue as it will use a huge amount of water every day. Check to be sure there is not an obstruction in the tank and if you can not find one, call the plumber. J.

Check to be sure small tube is flowing inside the ovefow tube. This is the water that flushes the rim holes, and refills the bowl. If you don't have flow clean or replace the float valve.

Sounds like your toilet is not vented properly. Possilbly something caught in the trap is causing it to syphon

You need to replace the tank flapper valve gasket.

First, fyi, adjusting the knob? in the tank, or the fill level will not increase the amount of water in the bowl. The bowl fills to a certain point, and then as more water is added it starts to go over the built in trap, and down the drain. When you flush the toilet, all the water in the tank dumps into the bowl, and the existing water is pushed over the trap and down the drain. All of this being said it sounds like you may either have an internal crack, between the bowl and trap; you may have a crack that is draining under your toilet, (water spots?), or you have a more serious plumbing issue, improper venting, which is causing a vacuum, and pulling the water out. Hope this helps.