From a ticketing/fares perspective, Old Street was included within the "London BR" station group (pre-privatisation equivalent of London Terminals) with effect from National Fares Manual 32 in January 1986. (Kensington Olympia was introduced at the same time, but was dropped from May 1994.) As to why: essentially, because it is a Zone 1 station, as noted above. (I know Kensington Olympia isn't, but there were other reasons for its inclusion.)
For context, some text from my unpublished research into station groups – second paragraph is particularly relevant: (The "As part of the progress..." part is a direct quote from the Manual.)
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The introduction of the pseudo-destination LONDON SR with effect from 26 April 1970 marked the first time British Rail had created a notional common location with its own National Location Code (5443) to cover multiple stations. Tickets issued to LONDON SR were valid to Blackfriars, Cannon Street, Charing Cross, Holborn Viaduct, London Bridge, Vauxhall, Victoria, Waterloo and Waterloo East. These were the Southern Region’s central London stations and termini at the time, hence the abbreviation “SR”. Tickets usually showed LONDON (S.R.) or LONDON (SR) at first to make the distinction clearer.
The concept was extended to the London termini of other Regions with the publication of Selective Prices Manual* 27 in May 1983: “As part of the progress towards simplification of routes and a reduction of entries [within the Manual], a common origin/destination of LONDON BR has been adopted for most London fares”. It was explained that tickets issued to this new pseudo-location could be used to travel from/to any of the 18 stations in the list, “subject to normal route availabilities” applicable to the origin or destination station. For example, Romford to Liverpool Street would be a reasonable route, and so would Romford to Fenchurch Street (via Upminster) and – in theory, at least – Romford to Broad Street (via Stratford); so a ticket from Romford to LONDON BR would be valid to any of those termini. It would not be valid to Marylebone or Waterloo, for example, because no reasonable route existed from Romford to those places using British Rail services only, and any possible route would be so convoluted that a much higher fare would be applicable.
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*The name for the National Fares Manual at the time.