Hotpoint WDAL 8640P washer-dryer is coating our clothes with lint

[Mustey]

It's a July-2015 washer-dryer.

Clothes often come out more dirty than they came in. They are covered with some very fine gray fiber that we take off using a roller sticker.
We tried:
- Cleaning the big rubber seal of the door 
- Cleaning the pump's filter (the one you have to pop the front lower lid off and turn it out, it was actually quite clean)
- Running the secret "A+B for 7 seconds" self-cleaning cycle
- Running an empty wash with washing machine cleaner
We get the fluffy stuff even if we don't run a dryer.

We are careful not to put lint-generating clothes in it (but maybe my lodger did that before).

It feels as if there is something that's storing this fuzz and it needs to be cleaned. I am wondering if I can do it myself because I live in
Newbury and it's an "all you can rip off buffet" for tradesmen here (our neighbor Reading has 2 or 3 times cheaper tradesmen).

Thanks for any ideas.

[Whitegoodshelp (Andy)]

Hello Mustey. Are you using good quality detergent and the correct quantity? Not using enough detergent can cause dirt to be redeposited on laundry. Also check this list out - Possible causes of washing not getting clean properly