My wife and I have been caravanners for over 20 years now, and we always have, and probably always will, stick to the same rule. We are both in our 40's, we both work, and we are both in emergency services where we see the appalling aftermath of accidents.
In answer to your question. NO speed doesn't matter. Getting to your destination by driving safely,legally and calmly is the objective.
Basically, the faster you go, the more at risk you become. Never do anything to upset the fine balance between travelling safely, and going fast for the sake of it.
You are pulling a caravan, and sudden UNEXPECTED changes in direction, for whatever reason, whether self induced, or caused by others, by mechanical defects,punctures, or by weather conditions, will always affect stability.
Every journey is different. Never get complacent when towing.
Never, ever drive if you are feeling tired. With a caravan, you can always get a couple of hours good rest anywhere.
When we set out on a journey with our caravan, we actually have a written 'check-list' that we go over before we even leave the drive. Tyre pressures, lights, skylights closed etc etc.
We travel at a speed that WE are comfortable with, according to road surface, weather and traffic conditions. We allow plenty of time, plenty of space between ourselves and the vehicle ahead of us, (double what you'd allow for a solo car), and we always book our pitch before we set off. If we find that we are getting traffic building up behind us, we pull off for a couple of minutes, as all caravanners should do. If we are running late, we ring the site. No problem.
The journey should be a pleasure, not a stressful ordeal.
Your initial comment "I am relatively inexperienced with towing" shows us all that you are a sensible guy, asking for advice, but then you went on to say.....which got us worried.....
"This weekend I overtook 3 outfits in a row which we travelling at 49/50mph on a duel carrigeway, I was doing 57mph ish." !!!
And you are 'relatively inexperienced' with towing ?
Steve has made a very good comment here, and which highlights a road surface condition which can cause SEVERE instability. That of 'tramlining' due to rutting on worn out roads. Hit that sort of surface at (57mph ish), and it could easily have you, your family, and your caravan and car off the road.
We live and work in the West Country between Torquay and Plymouth, and we see horrendous examples of how not to drive with a caravan, virtually every time we go to work. Some of the speeds that we see people towing caravans at are absolutely suicidal.
Almost all of the accidents involving caravans are caused by the driver losing control of his outfit, due to travelling at a speed where, when a situation has arisen, they were not able to cope with it. In other words, a sudden, and unexpected change of circumstances.
Punctures can and do happen. Idiots can and do carve you up. Sudden winds can and do suddenly blow your caravan. Big lorries will cause suction and instability, etc etc.
What speed others are doing is TOTALLY IRRELEVANT. Travel at a speed that YOU are comfortable with, and NEVER, EVER take your eyes off the road ahead. If something does crop up, then you will be able to handle it calmly and in good time.
Let the speed merchants, the tailgaters, the 'oh so important appointment' drivers, the know it alls, the clever Dicks and the smart Alecs get on with it. We've seen them all, and we've heard all the reasons.
They are usually spread all over the carriageway as we turn up with our blue lights flashing!!! And yes..... sadly, some of them do NOT go home again....................
And you know what? There's almost always somebody who will pull up behind the accident to drop them right in it!!!
Enjoy your caravanning.