Yes, vans towing touring trailers are common in the UK and Ireland - but they are mainly operated by Gypsy / Traveller groups; many coming from Ireland.
The Ford Transit, either as a van or in DRW flatbed configuration is a telltale sign.
The 3500kg and 7500kg weight limits are interesting and have changed over the years.
Until some time in the '90s a regular car license (like I have) covered you to drive any 4+ wheeled vehicle up to 7.5 tons gross weight.
However, a 30ft long, 8ft wide, 7.5 ton, cabover truck with air brakes and retarder is a bit different to drive to your average Ford Fiesta people learned in. So in the '90s they changed the rules. New drivers now have to pass an additional test to drive anything over 3.5 tons gross. At the same time they brought in tests for towing trailers, which also makes sense.
90% or more vans you see in Europe are under 3.5 tons for this reason.
I have considered buying a 7.5 ton 4x4 van which is basically an MDT with a van body on the top - giving a 4 ton payload - plenty of capacity for building a 4x4 camper. My driving license covers it. But there is still the question of other costs and restrictions.
Anything over 3.5 tons is subject to more expensive road and bridge tolls. I have heard of more than one European country either considering, introducing or already having an electronic road toll system where cars can buy a ticket, but vehicles > 3.5 tons are considered in the same category as 18-wheelers and need to rent or buy an electronic unit that charges by the km. This could turn out to be very expensive and inconvenient if travelling across Europe on vacation.
There are also many 3.5 ton weight limit signs appearing in villages or towns to prevent commercial trucks taking short cuts. Also, in the UK, all vehicles have to undergo an annual safety test. This is fairly cheap for cars and many garages offer the service. For vehicles over 3.5 tons I understand you have to go to an official government testing centre instead. I've heard of these being very picky about things (e.g. the orientation of signage on the rear of the vehicle).
Steve.