Xenon retrofit with no headlight washers?

Yes.

BMW OEM xenons would have come with auto levelling and washer system to be road legal in the EU. Most likely aftermarket if they don't have auto levelling and a washer system which is a requirement for the NCT. What year is the car? The later F20 facelift M Sport models were fitted with full LED headlights rather than xenons that didn't need a washer system.

By any chance are they HID bulbs rather than xenons?

So it's just a case of changing the bulbs for the NCT?

Worse case scenario just replace them with a set of high quality LED headlights. They pass the NCT without washers/levelling and are usually better quality than xenon.

Around €80 to €120 for high quality bulbs with warranty & fitting

An LED bulb is just as much a reason for a fail as an HID one - they're both considered to be incorrect if fitted to a halogen headlamp. I know people who have passed, and others who have failed - but they should be a fail.

Check - Compatibility (HID/LED bulb and headlamp). Fail reason - (m).Light source and lamp not compatible.

Although it doesn't even look like headlight cleaning is required for retrofitted systems anymore - although I wouldn't fancy having the argument with the tester, they can be pretty intransigent.

Headlamp cleaning devices are mandatory to be fitted with HID lamps with the exception of bulbs specified to produce 2000 lumens or less, retrofitted systems and vehicles which were not originally manufactured (type approved) for Europe

You should really post pictures of the headlights so we can figure out if its a genuine BMW Xenon headlight which was retrofitted, or just a HID bulb in the halogen unit.

I have heard of people failing - it’s the main reason I didn’t fit them to my E30 - and the NCT handbook says they’re a fail, so it’s down to the tester on the day if they’re not checking. I can’t be arsed arguing the toss with the inspectors at the NCT centre these days.

I had a lexus that had a faulty washer pump and failed. New pump and sorted. It was faulty for years and got through several NCT'S prior to the failure.

They can blind other drivers, so they should be changed out if they're not compliant.

LEDs can be fitted to reflector headlamps, as new LED emitters are small and sit in the same position as the previous tungsten filament, and so should be okay. Like below…

This other, cheaper style though, will throw light all over the place inside the reflector housing, and blind others, as will HID Xenon bulbs.

See how the light in the diagram below, all comes from a single point, and the reflector mirror is designed to accommodate that fact. If you were to place in the LED with multiple emitters (or a Xenon) the light would come from multiple sources and so reflect in lots of different directions.