I viewed a video of Geralt fighting the Maestro while drunk and every time the Maestro took a swing he simply stepped back avoiding the blow. For me Geralt did not respond to the movement keys and stood his ground, loosing the fight very quickly.
I have allocated the arrow keys as movement keys and must wonder if there is something I am missing as throughout
the game I have had trouble with fist fights.

You're having trouble because in fistfights you must dodge back - not move back. By default, the dodge keyboard key is "Alt" - but as you've adjusted the keybinding, you will have to go in and check what you have yours set for.

If it makes you feel better - I, too had frustration at the very beginning with fistfighting because movement was so sluggish. Using Dodge is the answer... wait until the opponent winds up for a big hit; block the hit and pummel him a few times. Then dodge back out of his reach... and repeat.

The only one I had any issue with was the Troll in Skellige for some reason. He took a ton of hits to wear down his health bar - and yet if he tagged me even once, I was dead instantly. Doable - but a very unforgiving fight.

I usually only use the roll key in a fight as it is more accessible than the dodge key.
So, to clarify, do I need to press the dodge key with the down arrow to take a step backwards
as I saw in the video?

Dodge automatically moves you back - you don't have to push any arrow key. In general (not just talking about fistfights) dodge is pretty much always very superior to rolling - unless you are trying to escape from many enemies at once. Winning brawls is not very hard really. Here is the "cheesy" way:

1. Dodge and move back for some distance.
2. Move quickly towards your enemy as this will usually trigger a big swing.
3. When they make the big swing counter attack so they lose their balance.
4. Throw a couple of punches until the opponent regains his/her balance.
5. Repeat step 1.

I never found the response to be slow, but I have seen so many people complain about it. Perhaps you are running the game at too high settings? I never experience any sluggishness.

Well, I suppose everyone has their own way, but I use the dodge key along with the "back" key ("S" for me - down arrow if you have that for the keybinding) to dodge back from a fistfight opponent.

So to clarify - Yes, use the dodge key as well as the down arrow key.

The standard "roll" just doesn't work effectively in a fistfight. It takes too long to respond while the dodge is immediate - and keeps you out of harms way...

Try it - play with different combinations to see what works best for your keyboard setup and your style. Jespergaard has the procedure nailed. Just stay out of their way until they wind up to throw a haymaker; block it; pummel them a few times; then dodge back out of their way. Repeat until they are down.

I finally succeeded. Geralt finally seemed to respond to the movement keys where previously he did not.
Strange.