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In addition to various property deeds, a variety of other documents survive relating to the estate of Furness Abbey at Butterilket (aka Brotherilkeld). These include charters giving the monks various rights, and financial records. Any that I find will be collected on this page:

A Papal Bull of 1247 (Pope Innocent) [quoted in Thomas A. Beck, in "Annales Furnesienses" (1844)] confirms Furness's property including "Brutherulkil"

John of Hudleston, overlord of Millom, grants to Furness Abbey the right to make stock barriers round the Butterilket/ Lingcove estate [From transcript in the Coucher Book of Furness Abbey, edited by John Brownbill, Chetham Society vol. 76, 1916]. Witnesses include: domino [=Master] Alano de Penyngton, domino Alano de Coupland, domino Ricardo de Brocton, Alexandro de Kirkeby, Willelmo de Twaytes, Hugone de Moricebi etc., so date is c1284-90.
...Johannes de Hodillston,
dominus de Millum in Coupland, salutem.
Cum abbas et conventus Furnesienses teneant
in foresta mea quasdam pasturas,
scilicet Botherulkil et Lyncoue, que quidem pasture sunt attingentes forestam domini de Egremund,
volo et concedo quod predicti abbas et monachi et eorum successores includant dictas pasturas
et eas inclusas teneant omni tempore anni,
sine perturbatione vel contradictione mei vel heredum meorum,
fossato, muro vel palicio prout predicti abbas et monachi
sibi judicaverint expedire;
ita tamen quod cervi et cerve et eorum fetus
dictas clausturas possint transilire...
...from John of Hudleston,
lord of Millom in Copeland, greetings.
As the abbot and convent of Furness hold,
within my forest, certain pastures,
specifically Butterilket and Lingcove, which pastures border on the forest of of the lord of Egremont,
I will and concede that the aforesaid abbot and monks, and their successors, shall inclose the said pastures,
and keep them inclosed at all times of year,
without disturbance or contradiction from me or my heirs,
ditched, walled or fenced as the aforesaid abbot and monks
themselves decide to make them;
but so that deer and does and their young
will be able to leap over the said barriers...

Agreement by Furness Abbey over John of Hudleston's rights to game animals [from the Coucher Book]. Date c1289-95, when William of Cockerham was abbot (it may well be contemporary with the previous document), (witnesses not listed in printed edition).
...Willelmus de Cokerham, abbas Furnesiensis,
et ejusdem loci conventus...
Noverit universitas vestra nos penitus renuntiasse
pro nobis et successoribus nostris in perpetuum
domino Johanni de Hodleston et heredibus suis omnimodas
venationes capiendas infra omnes liberas chaseas
predicti domini Johannis, ita quod fec nos
nec successores nostri aliquod jus vel clameum infra predictas chaseas de cetero in perpetuum ad venatione capiendas exigere poterimus vel vendicare;
salva nobis et successoribus nostris
in nostris propriis dominicis terris inter Esk et Doden chacea leporaria leporibus et vulpibus...
William of Cockerham, abbot of Furness,
and the convent of that place...
let it be known universally that we totally renounce
for ourselves and our successors, perpetually,
to master John of Hodleston and his heirs all [rights]
to take game animals within all the free chases
of the aforesaid master John, so that neither we,
nor our successors, shall be able to demand or justify any right or claim to take game within the rest of the aforesaid chases, in perpetuity,
reserving for ourselves and our successors
the [right to] hunt rabbits and hares and wolves in our own lordship lands between Esk and Duddon.

The Furness Abbey entry in the Taxatio Ecclesiastica [Church Taxation] granted by Pope Nicholas IV in 1292 [quoted in Beck] includes: "Item habent quandam vaccarium apud Botherulkull ubi recipiunt de fructibus animalium per annum, salva custodia, xxxiiij.s" [Item: they have a cattle farm at Butterilket where they receive, from the produce of the animals (allowing for the cost of looking after them) 34 shillings]

A charter of King Edward III, 20 Nov 1336 [See the Coucher Book edition] gives Furness Abbey the rights "De Warenna et Libero Transitu" [to keep rabbit warrens, and to move around without paying tolls] in their territories including "Boroudale, Botherulkle, Meles et Salthous".

A rent-roll of Abbot Roger (not necessarily Roger Pele, the last abbot of Furness?) [quoted in Beck] includes: "Item Brotherykell... vj.s viii.d" [£5 6s 8d], also among the deductions: "Item Johanni Huddylston pro Brotheryleketh... v.s" [5s; John Huddleston was Lord of Millom, and Butterilket was within his administrative area]

At the Dissolution of the Monasteries, Furness Abbey and its possessions were surrendered to the state on 9 April 1537, and temporarily administered as part of the Duchy of Lancaster, by Christopher Sandes, bailiff at Millom. Rent-roll information from this period [quoted in Beck] includes: