Why are “Wire Nuts” not used in the UK?
In Brief


Twist-on connectors have a bad history in the UK.
The UK traditionally relies on screw-terminal connectors.
UK Electricians are conservative.
UK junction boxes, switches, ceiling-roses etc contain enough built-in connectors that additional loose connectors are not normally needed.
Newer types of lever-action, squeeze-to-open or stab connector blocks are possibly more popular alternatives.


Twist-on connectors

The Wikipedia article on twist-on connectors suggests they were outlawed in the UK 50 years ago. No references are given. It is suggested that 50 years ago the ("Scruit" brand) twist-on connectors were made of ceramic and were liable to crack and expose the wires.

UK Electricians are a conservative group. Vendors of novel products have to go to considerable length to persuade them that their products meet the relevant legislation.

An Ideal Industries Inc. catalogue says


  Conforming to BS EN 60998 Twister® wire connectors fully 
  comply with BS 7671:2008 (17th Edition Wiring Regulations).


However, it isn't uncommon to see strenuous efforts on the part of manufacturers to persuade UK electricians that novel products meet regulations. E.g. Wagobox and Ezybond earth fasteners Some of these novel products more or less disappear from the market within a few years, others succeed.



Screw-terminal-blocks

In the UK, electricians almost invariably use screw-terminals.


ruler is marked in cm with mm subdivisions

The white translucent screw-connector block in the foreground is a typical example. This one is rated for 5A. Other sizes are available for different current ratings. 

An electrician left behind the other connectors in this picture. I suspect they were used for temporary connections during installation. I've not seen any in a completed installation (but I'm only a householder not an electrician, so have very limited experience)

The "Marr No.1" connectors at back right  look superficially similar to US wire-nuts but are very different. The metal insert is removed and a grub nut is used to clamp the wires, then the plastic insulator is screwed over the connection.

The "Legrand 10mm2" connectors at top left may be for higher current ratings. Note that the plate that presses on the wires is arranged so as not to exert any twisting force on the conductors. Perhaps this avoids damaging stranded conductors. It certainly prevents the conductors being pressed to one side of the screw and therefore not being securely clamped in place.

An obvious advantage of these connectors is that the wires can be removed intact and should usually not need trimming before reconnection. I have the impression that in the US, wire-nut connections are often removed by cutting the wires, which may leave progressively less and less wire available in the junction-box or back-box for remaking connections.

When more than two wires are to be joined, a slightly different type of screw-connector is used:



Switches, junction boxes and ceiling roses often contain sufficient bult in capacity that you don't need additional connectors:



Newer connectors

Easier-to-use connectors are becoming more common:



Some of these are "lighting connectors" used to join solid-core wires to stranded wires. They are all rated at 20A and at least 300V. They all incorporate a test-port and wire-trimming guide. 

It may be that UK electricians looking for novel connectors prefer these to twist-on connectors.