Our WM2016CW machine's drain hose has a wire mesh filter on the end of it. The drain hose then is attached to a drain pipe which used to be connected to an old sink (no longer there). Is this mesh

Although you have not shared the make, model, and year, I will give it a try anyway.
Start by turning off the water at the faucets for the washer.
Then unhook the hose ( or both of them) and attach a garden hose to the faucet, and run the hose outside, or if that is not possible, run the hose to a sink or a shower or a tub, for the drain.
Turn on the water faucet and see if you get good pressure through the water hose.
If you do, then examine the black hoses from the faucets to the washer.
Often these have a tiny wire mesh filters inside the end or ends of them to filter the incoming water.
These can plug up with sediment, and you will need to clean them.
If they are clear, then examine the attachment on the back of the washer, where the hoses go.
These can also have tiny wire mesh filters inside, that can plug up with sediment.
Those screens can be removed and cleaned.
God bless your efforts.

pump blockage or pump

Hi if you remove the pump again get a plug and wires example from a table lamp and attach 2 wires to the pump dont worry about polarity it will run both ways plug into the wall see if the pump runs out of the machine ( does this model have 2 pumps one could be the recirculation pump)

it is a drain hose so there is no need for a filter
the water to drain will be dirty so there is no point in filtering dirty water destined too go down the drain

F05 - Pressure switch jammed on full - Book a washing machine repair.

Was what the manual said. But then I found this write up from another source:

Drain machine by running the outlet pipe into a bucket at floor level or run the outlet pipe out of the back door if it'll reach. Check the filter unit for blockages. Filter generally located behind a panel at the foot of the machine.Some are obvious like little square hatches and some are hidden behind the trim panel at the foot of the machine. Once panel is removed the filter should be visible. Its generally a circular plastic fitting which unscrews in an anticlockwise direction. Some hotpoint, indesit and ariston filters are located in the big black sump hose (the one that leaves the bottom of the outer drum and connects to the pump). Remove the back cover, locate hose, remove the tensioner clip by squeezing the tabs together with a set of heavy pliers or vise grips, remove the hose, take out filter and clean. Be prepared for spillage of water. May help if the machine is tilted backwards at an angle.
If problem persists, check pump and pump hose. Pump removal: power off, drag machine out onto the floor, remove back cover or tip machine up at an angle, locate pump, (attached to other end of drain pipe).undo 2 wiring connections, 2 hose connections, and pump mounting screws. Remove pump chamber - some are held in with screws, others clip into place. Check for foreign objects round the impeller. If pump chamber is clear, may be a fault with the pump motor - in which case, replace the pump.

Repair and service your own washing machine. Go to www.2ndwave.co.uk/manual.html

Open the little door in the bottom left hand corner, unscrew the black cap and drain the water out.
If this doesn't fix the problem, you may need a new Drain pump. Unplug the machine. Remove the filter recess by removing the one screw inside and using a putty knife at the left and / or right edge and popping it out. Pull the machine out about 18 inches and tip it back, resting it against the wall. Remove two more screws behind where the recess was holding the pump housing on. Reach under the machine and remove pump. There is a tab to depress under the pump housing to release it from the base. The pump motor is held onto the housing by three screws. Remove them and inspect the impeller to see if it has come off the shaft. If it has, pushing it back on will not solve the problem, as it will come off again. Install new drain pump and reassemble.

I’m happy to help further over the phone at https://www.6ya.com/expert/jeremy_69f3cc28d95bf514

that is basically what it does
stops coins buttons bra wires etc
most washing machines have a section in the pipe before the pump where the hose comes out a few inches above the bottom and this is like a trap where objects fall and are retained
as most machines are difficult to get to the hose or pump , having a filter there is a bit impracticable as you would be cleaning it every other wash
if your machnie doesn't have an end trap arrangement you could improvise such a unit using a "T" section of plastic pipe with the hose on one end , a cap on the other and the hose to the pump from the middle

Following a 1E error I found the gaskets in both supply hoses had perished and the debris had blocked the mesh inlet filters, causing the grinding noise that the pump makes when it can't get water. The original LG filters are indeed removable, in bits. Their little plastic tag for pulling them out snaps off so you end up digging the filter out, just be careful 'cos there's another mesh behind the filter on the hot and there's a rubber seal behind the cold one. Easiest thing is to forget replacing them with original parts and get the old fashioned kind from Lowes etc, $2 for a 3 pack, these fit into the end of the supply hose and are a rubber gasket with mesh in the middle so you won't even need to buy gaskets to replace the ones that fell apart.