My toile tank does not completly flush, I have to hold the lever up untill all the water in the tank emptys and complete flushing occures. What is the solution?.

Shorten the chain on the lever, to much slack won’t pull float high enough.

allow tank to fill a little more by adjusting fill valve. When there's not enough water flowing from tank the stopper can over-power the water flow and cause the flush to stop by re-sealing.

replace the flushing controls or install a new cistern

Wiith all due respect, the Drake toilet is not a regular toilet and doesn't sound the same as a regular toilet when you flush it. It is in the design that allows it use only 1.5 gpf instead of 3.5 gpf. A rather unique thing is that while it is scientifically calibrated to release 1.5 gpf, it does not empty the tank of approximately 1 gallon of water. Therefore if one feels the need for a little extra umph, simply hold down the flush lever when you flush until the tank is emptied.

Not being a plumber by trade I don't want to bad mouth what your plumber had to say but there may be other things to consider.
If the toilet does not flush directly into the main drain there is the possibilty that the coupling between the main drain and the toilet drain is under-sized which could cause reduced water flow and your toilet not flushing completely.

Assuming we are talking about a standard flush toilet, it sounds like the internal flush actuator lever is hitting the top of the toilet on the inside. Remove the lid, hold the exterior handle. and carefully bend the lever down a little. Also make sure the lever hasn't slipped or is loose. Put the lid back on try again. Repeat until the toilet flushes with the lid on.

Some of these come with a flapper/flush valve that is made to operate in partial or full flush. Look at the underside of the flapper. Is it a cone shape that has a pencil sized hole in it (or two)? This cone is supposed to keep the flapper afloat during the flush, but the holes allow it to flap back down early. Its a pretty cheezy way to pass the low water requirement, but they get away with it. If you hold the flush handle down for a few seconds (until the tank empties) you will get a full flush, but only when you need it. Or you can just buy a replacement flapper that doesn't have the hole in it. They are cheap and easy to replace, but you will use more water.

Just a thought, you might try to get a piece of chain at a hardware store and do it yourself.....might cost $3, maybe less. There is also a screw on the top of the lever the chain and float are attached to, you can loosen or tight it to change the way the toilet flushes.
You can also check on line at:
www.howthingswork.com

hello, this is a standard toilet you will need to inspect the flapper that is the rubber flap that holds the water up in the tank it works when you pull the lever it pulls the chain upward and lets the water flow if this flapper is old it may not stay up long enough for the water to flow. open the tank top and flush the toilet see if this flapper is staying up long enough and giving the tank enough time to empty if not change this rubber flapper its inexpensive part.
if this is not the reason then you need to adjust your water filler valve there should be a small screw on top of the pivoting float arm
if you have to adjust it for the water limit line inside the tank this will be the proper amount of water needed to flush once completely

also check that the chain lenth on the pull lever is not pulling the flapper down quicker than its supposed to,

try this let me know your results
hope it helps