BE term for a historical type of outlaw?

This is not an easy question to answer. I hope others may refute my final conclusion.

Outlaw = a person who has broken the law and who lives separately from the other parts of society because they want to escape legal punishment

Cambridge dictionary

It is relevant that this is a very old term:

outlaw (n.) Old English utlaga "one put outside the law" (and thereby deprived of its benefits and protections), from a Scandinavian source such as Old Norse utlagi (n.) "outlaw," from utlagr (adj.) "outlawed, banished," from ut "out" (see out (adv.)) + *lagu, plural of lag "law" (see law). Formerly it was lawful for anyone to kill such a person. [G]if he man to deaðe gefylle, beo he þonne utlah ["Laws of Edward & Guthrum," c.924] Meaning "disorderly person living in defiant violation of the law, one living a lawless life" is recorded by 1880. As an adjective, from Old English. outlaw (v.) Old English utlagian "to banish, proscribe, declare an outlaw; to deprive (someone) of the benefits and protections of the law," from utlaga "an outlaw" (see outlaw (n.)). Related: Outlawed; outlawing.

Etymology online

The antiquity and persistence of the word seem to have worked together to provide an umbrella of meaning for many other words that might be seen as synonyms but on examination prove to be words with associated or consequential meaning rather than synonymous meaning.

For examples: fugitive (not necessarily an outlaw); bandit (not necessarily outlawed); highwayman (some were outlaws, some outlaws were highwaymen); pariah (despised and rejected but not necessarily outlawed). The list of such near but imperfect synonyms is long.

Consequently, I suggest that there is no outstanding alternative.

There is one ancient English tradition known as caput lupinum, or "wolf's head":

CAPUT LUPINUM, Eng. law. Having the head of a wolf. An outlawed felon was said to have the head of a wolf, and might have been killed by any one legally. Now, such killing would be murder. 1. Hale, Pl. C. 497. The rules of the common law on this subject are much more severe in their consequences, than the doctrine of the civil law relating to civil death. See 1 Toull. Droit Civil, n. 280, and pp. 254-5, note 3.
_{TFD Online}

This would place the outlaw beyond legal process, in a "wanted dead or a live" context.

BE term for a historical type of outlaw?

There is only one type of outlaw - any criminal (and later defendant) who has been declared outlaw.

The outlaw is set against a background of a separate criminal offence: First you committed the offence and then you were declared outlaw, i.e. you could not benefit from the law - the law would not protect you from anything anyone else did to you. The usual result of this was that you would flee to some place where you were not known, and then never return to the area of the crime.

1895 F. Pollock & F. W. Maitland Hist. Eng. Law I. 27 Before the Conquest, [of England by the Normans in 1066 AD] outlawry involved not only forfeiture of goods to the king, but liability to be killed with impunity.

[...] [ibid]. 459 [In the 13th c.] outlawry loses some of its gravity; instead of being a substantive punishment, it becomes mere ‘criminal process’, a means of compelling persons to stand their trial.

It was then used for misdemeanours and civil actions and prevented the outlawed person (the outlaw) from bringing an action for his own benefit against someone in court.

In the UK, it was partly abolished in 1879 and completely abolished in 1938.

A. n.

1.a. Law. A person declared to be outside the law and deprived of its benefits and protection; a person under sentence of outlawry (outlawry n.). Also figurative. Now chiefly historical.

First recorded in the 9th century

1990 W. I. Miller Bloodtaking & Peacemaking vii. 238 An outlawry judgment isolated the vengeance target and eroded his support. Any assistance granted to an outlaw was itself actionable.

1.b. A person who lives without regard for the law; a miscreant, felon, criminal, esp. one on the run from a law enforcement agency. In early use, frequently indistinguishable from senses A. 1a and A. 1c.

First recoded at the end of the 12th century

1991 D. Gaines Teenage Wasteland viii. 199 An ‘electronic underground’ of message boards, where computer-literate outlaws share pilfered credit card numbers [etc.].

1.c. A person who has been banished or proscribed; an exile, a fugitive. Now rare, except as in sense A. 1b. In early use, not distinguishable from sense A. 1a.

First recorded c 1225

1964 N. Mandela Struggle is my Life (1978) ii. xii. 166 I naturally found Rivonia an ideal place for the man who lived the life of an outlaw.

†2. The action or process of being made an outlaw; sentence or proclamation of outlawry. Obsolete.

First recorded a1382

1652 J. Wadsworth tr. P. de Sandoval Civil Wars Spain 115 Hee made publick Acts, Proclamations and Out-laws against the Segovians.

(Quotes via or from the OED.)