To let your readers know a little more, which may help them to identify Margaret.
Sidney Stephen (1797-1858) was born at Somerleage, Somerset, England (although that conflicts with his Find A Grave memorial, which has Tortola see at end).
He became Chief Justice of New Zealand.
News came from Hobart in 1850 that he had been appointed Judge of the Supreme Court in Otago. He was to be Judge and Deputy in the office of Vice-Admiralty in the Southern District. The Government Gazette announced in Aug 1850 that he was to be a third judge, implying an addition expenditure of public money of £1,000-£1,200 (around $130,000 today)

Their 3rd son, Henry George Stephen died in Melbourne of scarlet fever on 10 Jan 1851 aged 21. These touching words were in the Melbourne Morning Herald 14 Jan ..
Yet even joy and beauty's bloom,
And hope that dazzles in the eye,
Are blossoms gathered for the tomb -
Soon, soon to died
Just in the morning of his day
As young as we he died

The Proclamation from the Government Gazette, 24 March 1851 (in part) ..
By His Excellency Sir George Grey, K.C.B., Governor-in-Chief in and over the Islands of New Zealand and Governor of the Provinces of New Ulster and New Munster and Vice-Admiral of the same, &c., &c., &c. WHEREAS by an Ordinance enacted by the Governor of New Zealand, with the advice and consent of the Legislative Council, Session 3, No 1, intituled 'An Ordinance for establishing a Supreme Court' the Governor of New Zealand is empowered, with the advice of the Executive Council, by Proclamation from time, to divide the Colony into districts for the purposes of the said recited Ordinance and the limits of such districts from time to time to alter as occasion may require.
And whereas, by Proclamation dated the thirtieth day of July, One thousand eight hundred and Fifty, the said colony was divided into three districts, named respectively the Norther, Middle and Southern districts, whereof the Southern district was assigned to SIDNEY STEPHEN Esquire, A Judge of the Supreme Court.

In Nov 1853 His Excellency The Governor was pleased to appoint His Honor Sidney Stephen, a Judge of the Supreme Court of New Zealand, to be a Trustee of the lands granted as an endowment for a College and Grammar Schools in the Town of Wellington

In Oct 1855 His Excellency the Governor appointed Sidney Stephen Esq., to be Chief Justice of the Northern District and Daniel Wakfield Esq., Judge of the Southern District, during the absence of William Martin, Esq.

In Feb 1856 he had the title His Honour Sidney Stephen and His Honour the Acting Chief justice for the Northern District

In May 1857 he was appointed Judge of the Southern Provinces, in place of Daniel Wakefield who was incapable due to illness.

In Oct 1857 Sidney was congratulated, at the opening of Court, on his restoration to health and his resumption of duties after his severe indisposition.

NZ Gazette, 13 Jan 1858
HIS HONOR CHIEF JUSTICE STEPHEN It is this day our painful duty to record an event, the first of its kind that has occurred in this colony. Sydney Stephen Esq., Acting Chief Justice of New Zealand, has been removed from amongst us - struck, it might almost be said "in the very seat of judgement," not indeed by human hand, for in these days "the majesty and power of law and justice" are respected in the highest places - but by the inevitable hand of death. It is well known to our readers that his Honor had been for some time ill and unable to attend fully to his judicial duties, but we believe that few anticipated that his earthly career was to close so soon.
The Acting Chief Justice died on Wednesday morning, the 13th instant, at 10 o'clock - aged 61 years.
Sydney Stephen, Esq., the subject of our present notice, was one of a numerous family, all more or less celebrated for their legal attainments and possessing a historic name and influence in the annals of Australasia. He was the son of John Stephen, Esq, for some time Puisne Judge of New South Wales and his surviving brother, Sir Alfred Stephen, the present Chief Justice of that Colony, having filled the offices of Solicitor-General and Attorney General of Tasmania (under the able administration of the late Sir George Arthur) from when he was promoted by the force of his ability to the Australian Bench. He was called to the bar of the Inner Temple in the year 1818 - being then about 21 years of age. Through the influence of Sir James Stephen, the well known essayist and statesman, who so long ruled the Colonies as Under Secretary of State, he was appointed Attorney-Secretary of State and he was appointed Attorney-General of St Kitts in the West Indies, which office he resigned, after having filled it with much success and popularity for about five years.
From St Kitts he went to Port Phillip, where he practised at the bar for some time and then proceeded to Launceston. For several years the deceased Judge was a practising Barrister in Hobart Town until he came into unfortunate collision with Judge Algernon Montague, a man of an ungovernable and over-bearing temper, who, although junior to him at the bar, inhibited him from practising in any court of law in the colony as Mr Stephen was capriciously and as it proved, unjustifiably, disbarred. The case being referred home, the Judge was severely reprimanded and Mr Stephen re-instated in his former position. We may add with reference to this affair, that the general opinion of the legal profession was that but a faint measure of justice had been rendered to Mr Stephen and that compensation was due to him from the Judge, for the loss he had sustained during the time that the matter was under the consideration of the Imperial Government.
From Tasmania, Mr Stephen came to Wellington, New Zealand, having obtained through the influence, as we are informed, of the Colonial Secretary, Mr Chapman, the appointment of Puisne Judge at Wellington; from which office he was removed to supply the place of Chief Justice Martin, whom ill health compelled to resign his office and to leave the Colony.
Last winter, Mr Stephen laboured under a very severe illness, his life at that time being despaired of. He rallied, however and resumed his post on the Bench at the last Criminal Session. But it was painfully evident that his health was seriously shattered and subsequent postponements of the Civil Sittings showed that his strength was unequal to the duties that were required of him - for he sank, as we have already stated, on Wednesday.
We cannot close this notice of one who has occupied so high a position in the Colony, without adverting to some of those qualities of mind and of heart for which he was distinguished. First of these, was his thorough independence as Judge; and second - what many of our humbler readers will consider to be first, as it is the one that endears him most to their memory - his readiness, at all times, to give advice to the poorer classes, to whom the processes and technicalities of the law, were, apparently, an effectual bar to the impartial administration of justice. That these are not mere words of fulsome panegyric, our local readers, many of the with tears, will readily testify.

The ceremony of the Funeral will take place on Friday, the 15th instant, when the presence of a Public Functionaries of the Colonial Government is required and the attendance of all other persons who may be desirous of testifying their respect, is requested.
The funeral will leave the residence of the late Judge, Albert Street, at five o'clock p.m.

Sidney was buried at Symonds Street Cemetery, Auckland (with his photo)

also see The STEPHEN FAMILY, Australian legal family

The children of Sidney & Margaret:
1821 - 1875 Sidney James Stephen
1823 - 1895 Francis John Sidney 'Frank' Stephen
1825 - 1890 Mary Ann Sibella Stephen
1827 - Elizabeth Mary Milner Stephen
1829 - 1851 Henry George Alfred Stephen
1831 - William Henry Stephen
1833 - Margaret Louisa Stephen
1835 - Cecilia Boon Stephen
1836 - Alfred Frederick Stephen
1841 - Zoe Francesa Sophia Stephen

Margaret Stephen (nee Adlam, 1800-1875) died 17 May 1875 and is buried at St Kilda Cemetery (with photo) with their son Sidney. Has that she was born at St Kitts. In Sidney's bio link it has that she was a daughter of a St Kitts merchant, Alexander Adlam

Thank you Ngairedith for your informative post. Sidney STEPHEN was born in Tortola. It seems that 2 of his siblings, Mary Ann and Clara were born in Summerleaze, near Wells, Somerset.

Margaret ADLAM is my brick wall, having no further information, other than her name and possible father's name of Alexander. It seems that Sidney and Margaret married in the West Indies.

I know that there are many ADLAM's in NZ but I have no idea if any of them would be related to Margaret.

Regards,
Ronmar