Wall fixings are usually not a problem, there are loads of types. Nor is a post at the other end, there are various options with ground anchoring.
If there is a problem, it will be with the washing line itself. Twelve metres of wet washing can weigh heavy and with UV degradation and wind load of the usual PVC coated thin nylon lines they will eventually break especially near cleats etc., where they rub. You may be better with an intermediate post i.e. 2 x 6M; make the middle one removable with a ground tube insert.

The question refers to a pulley line system, not simply an ordinary single line.
I can't see an ordinary plastic-coated line working satisfactorily because of the difficulty of making the attachment each time to the cleat - it's hard enough tying a secure permanent knot, the stuff is so intractible, slippery, and prone to cracking round tight bends.

I thought the point of a pulley system was so that you could add or remove washing from one end, such as an upstairs window, without having access further down the line. A prop part way along wouldn't work, for obvious reasons.
I'd have you needed something sturdier yet flexible, from a yacht chandlers perhaps.

I assume the line is perpendicular to the wall, if so then some sort of plate with an eye and three or four fixing may be OK but you could also go for a shield anchor with an eye instead of a hex bolt head. Then buy a pulley with an eye ( literally 1000s to choose from in every material you can think of and for many rope sizes ). Then all you need is a shackle to join them plus a wall cleat. There are other variations on this theme.
At the other end it's easier to fix a snap hook on the line, with an eye on the post to attach it to, rather than tying and untying each time.
P.S. that's how I did something similar, and all the hardware in SS was quite cheap.

Posted By: djhIs the line too high and needs to be let down to un/load it? Or is it loaded from e.g. a balcony and needs to be pulled around to un/load it? Or something else?

An Answer to this question would help in giving a solution.

Posted By: djhBTW, I'd think a normal steel-cored line would be flexible enough to go around a pulley of a decent diameter and won't stretch much, but do check.

The rule of thumb for wire ropes and pulleys is 20 x dia of rope is the minimum pulley size (but bigger if the rope goes more than 90 deg. around the pulley).

A trip to the dinghy chandlers will show all manner of pulleys, shackles cleats etc. all in stainless steel and they will also probably sell kevlar based rope and cordage which will not stretch under load and IMO is better than the plastic coated wire stuff sold for washing lines (no plastic coating to crack off after time in the sun)

The line will be 3.5m up in the air

So lifting it, but also making it easy for the wife to pull up...

It is simple enough to reduce the effort needed to lift up the loaded line by use of a pulley giving a 2:1 ratio that will reduce the effort needed by 50%.
On the attached diagram a pulley is attached to the end of the washing line and a line passed through this, one end of which is fixed to the wall and the other end is pulled to raise the line and then tied off. The 2:1 ratio works when the line is pulled vertically downwards. If the line is pulled out at an angle the advantage is progressively lost as the angle away from vertical increases.

Something like https://www.marinesuppliesdirect.co.uk/8-plait-pre-stretched-polyester-rope-white-4mm-or-5mm-1532-p.asp if you don't like the plastic coated.
If/when it gets grubby, put it in an old pillowcase tied up with some string and put in the washing machine. Loads strong enough etc.
Don't stress over size of the pulley wheel (sheave) - as long as it is not tiny it will be fine.
Somewhere like https://www.gsproducts.co.uk/pulley/ for pulleys (blocks) maybe