Hi George,
I think you are entirely right to assure yourself about the provenance and possible copyright status of any image you find on the internet. Assuming that you are reasonably sure that this photograph was produced by a British photographer (probably a professional working in a high street establishment) then we need to look at the copyright issues in terms of the 1862 Fine Art Copyright Act which was the law at the time that the photograph was made, and then look at the subsequent legislation to see if this altered the situation.
Photographs from around this era were treated as special cases and were not given the same level of respect or protection compared to, for instance, fine art such as a painting or an engraving. In fact the 1862 Act was the first time that photographs became eligible for any copyright protection. The term of protection was the lifetime of the photographer plus seven years after his death, provided that the photograph was registered with the Stationers Company in London. As you may imagine, many photographs were never registered due to the cost involved (a shilling) and the inconvenience of the registration process, especially for photographers based outside the capital. The bulk of the work of the social photographers of that time consisted of personal commissions for portraits of their clients, and under the law of the time, copyright would automatically transfer to the commissioner. Thus the photographer had no interest in establishing the copyright through registration, and his clients would either be ignorant of the requirement or would have seen it as unnecessary since such portraits tended to be for private use only. Registration therefore tended to be confined to photographs which were intended to be published commercially in books, postcards or magazines etc.
In 1886 Britain became a signatory to the Berne Convention which was an international treaty between a number of mainly European nations concerning the reciprocal treatment of copyright works between the signatories. This convention stipulated, among other things, that there should be no 'formalities' in order to gain copyright. However photographs were not initially included as works worthy of protection and they were not added to the Convention until 1908. This meant that Britain had to abandon its practice of registration, and so a new Copyright Act was passed by Parliament in 1911.
Section 21 of this Act said that all photographs were to be protected by copyright for 50 years from the date they were made, and then such protection would cease. This provision applied to all photographs which were still in copyright at the time that the 1911 Act came into force. So assuming the particular photograph you are interested in had been registered at the Stationers Company, it would have qualified for the new regime after 1911. If the image was made around 1900 it would thus have ceased to be protected at the end of 1950. Even if it was made later than 1900 (say sometime before 1920) then it would have ceased to be in copyright long before the more modern rules came into force in 1988. If it was never registered, then it was never entitled to any copyright protection, assuming the image was made before 1911.
So I think you can rest assured that a photograph from that era would now be out of copyright. It is worth noting that this situation only applied to photographs. From 1911, other works such as works of literature, music or fine art etc were protected for the lifetime of the author, composer or artist plus 50 years from the end of the year of their death. In 1995 this term was extended to the current period of the lifetime of the author plus 70 years thereafter, meaning that many works from the 1900s, other than photographs, could well still be in copyright today.