United Kingdom Slide rules and logarithms (the mathematical basis of slide rules) were invented here. Whilst there was a large range of manufacturers they do not seem to have had the wide export penetration that one might expect.
Maker	Model	Notes		Origin
Emblem	1053	A learner's rule with two hair lines for different horse power.
PIC/Thornton	Junior	A basic rule with trig scales on back of slide	Full instructions.
PIC/Thornton	111	A basic rule with Thornton's patented trig scales.	Full instructions.
PIC/Thornton	121	My own rule from school and university	Full instructions.
PIC/Thornton	131	An electrical rule
PIC/Thornton	3649	Did not use Thornton's patented trig scales.	Full instructions.
PIC/Thornton	3654	An early Thornton with two cursors.	Full instructions.
Thornton	AD 050 Log-log	A popular model in Britain	Full instructions.
Thornton	AD 060 Standard	A popular student's rule	Full instructions.
Thornton	P 221 comprehensive	Two different types of trig scales on one rule!	Full instructions.
Unique	Log-log	A cheap and popular model
Unique	Electrical	Includes scales for temperature/resistance relationships	Instructions available.
Unique	Universal	Three versions of this rule are shown.
Unique	Navigational	Designed, as its name suggests, for navigational use.	Instructions available
Unique	Brighton	Designed for the continental European market.
Unique	Study 500	A late rule with unusual scale set.
Davis	Autocrat	An early British rule.
The Technical	Standard	Another early British rule.
Boots Ringplan	Ringplan precision log-log	This rule has four log log scales plus other rare ones.
Helix	Top precision A101	An example of a badly designed rule
W H Smith Log-log trig	Log-log trig	Included because of the shape of its instructions
Dargue	Simplon Primary	A fairly basic rule
Dargue	Simplon Major log-log	Has some unusual features including a bevelled slide.
Dargue	Simplon SR10 bilateral	Cursor can be reversed to use both faces of stock.
Blundell	808 Accountants	A rule designed for calculations in pounds, shillings and pence.
Blundell	Classmate 813	A student's rule
Blundell	Duplex 904	A compact rule
Blundell	Reitz 803	A straightforward version of the classic "Reitz" configuration.
Blundell	Omega 410	The rule has an A but no B scale.
Blundell	Super Duplex A506	One of the rare rules with hyperbolic functions.
Blundell	AG5	Probably for artillery use.
Hardmuth	Classic Series IV	Used a similar construction to Unique rules.
MDS	System Rietz	A German made rule but an  English supplier.

Notes:
Original instructions: scanned version of maker's original instructions
Full instructions: complete instructions based on book or similar.
Instructions: instructions based on my own research.
For some rules instructions are given for special scales only.