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I have fjallraven barents pro trousers, with knee pads. The pads enter the trouser, where they open at the bottom of the kneecap, and you can buy foam knee inserts for a tenner to put in there. They dry quickly, and are hard wearing. They could be improved in my opinion by zips in a few pockets. Expensive though.
Or you could buy cheap knee foam pads, that tradesmen use, and some cheap austrian army trousers, from endicotts for about £12.
5.11 stryke pants are my current favourites, loads of pockets but not excessively tactical looking and pretty tough and comfortable. Sadly over budget though and probably wouldn't pass the camp fire test although I've happily not had a problem in that regard with any trousers to date.
I've been using tradesman trousers from Dickies for awhile with work; have worn them occasionally in the woods and they would fit the bill. Meet all your criteria and they're still available as black/brown combo. Paid around £22 for mine
In brown... you might find the odd Travis Perkins or similar with old stock in (I did... mine were £12.99 a pair so I bought 2 pairs)
Pros: Harder wearing than just about anything else I've tried, huge array of pockets, clip loops etc, very strong belt loops, drop in knee pad pockets instead of push up ones
Cons: Heavy, might have too many pockets for someone who is pocketist.