WS Barring-Gould created a third brother to explain why Mycroft was working in London and not home minding the country estate. Barring-Gould assumes two positions regarding this mysterious third brother:
1) The Holmes family are upperclass
2) there is a country estate
Sherlock refers to his ancestors as being country squires who lived much as country squires did. It’s entirely possible this is suggesting like a lot of the upperclass landowners there were mis-investments, money being squandered and a family line being beset with all sorts of financial and interpersonal issues. Anyone who watches Downton Abbey will be familiar with the story of a family where there were no immediate male heirs. There could have once been a country estate, but not one Mycroft inherited.
Additionally, Barring-Gould is keen on the idea of the Holmes brothers being upperclass. It’s possible they were not. Mycroft would have joined the civil service following the results of the 1854 Northcote-Trevelyan report. This report criticised the civil service for being a dumping ground of the sons of the upperclass who did not demonstrate the kind of pioneering attitude Britian needed to oversee its colonial interests, the report recommended an end to nepotism and suggested the Chinese method of recruitment where potential candidates took an exam to secure their appointment. It wasn’t until the 1870s that the recommendations of the report were being put into place, by this time Mycroft would have been done with university and very likely would have found himself taking further exams to secure his employment as Ronald Knox* suggests as clerk in an unmentioned branched of government, before rising to his position as the British Government by the time Holmes and Watson meet. Oxbridge would not have been a barrier to the middle class Holmes brothers who could have benefited from patronage, something the Anglican church often did. Sherlock is quite enthusiastic about the board schools, “Beacons of the future! Capsules with hundreds of bright little seeds in each, out of which will spring the wiser, better England of the future.” As he’s a man who sees education for all as the future perhaps because this suggests own education was paid for by charitable or philanthropic means. Fittingly, this quote comes from ‘The Naval Treaty‘ which could be read as Conan Doyle’s commentary on the civil service – Percy Phelps, through his uncle Lord Holdhurst secured a position in the foreign office, looses an important document and has an epic breakdown as a result.
Of course, there’s also nothing to say Mycroft was managing the country estate and spent his weekends there checking up on things.
(*’The Mystery of Mycroft’ by Ronald A Knox, possibly published in 1934 – not sure but it’s definitely in HW Bell’s 1934 collection of essays ‘Baker Street Studies‘)