There seems to be much misunderstanding about these speakers and, as a consequence, an awful lot of hype and cult status has followed.
First it must be understood that the speaker was designed by the BBC, as they were looking for a near field monitor that could be used in their OB television control-rooms.
The BBC document: BBC RD 1976/29 "The design of the miniature monitoring loudspeaker type LS3/5A" by H.D. Harwood, M. E. Whatton and R. W. Mills (available on the web) makes this clear.
Quoting from the introduction:
"There is a need to monitor sound programme quality in circumstances where space is at a premium and where headphones are not considered satisfactory. Such circumstances include the production-control section of a television mobile control-room, where the producer responsible for the overall production of the programme needs to monitor the output from the sound mixer but at lower levels than those used for mixing." (The emphasis is mine)
Despite using the KEF B110 unit in a small enclosure, the loudspeaker has a response that is substantially uniform down to 100Hz. In the design the bass unit is overdamped.
Measurements made at a distance of 1.5m (a typical listening distance for a near field design) and at a SPL of 70dB show a response flat to +/- 5dB. Distortion measurements were made at an SPL of 88dB (ref. threshold of hearing). This gives an idea of the sound pressure levels expected.
It is thus to be expected that the LS3/5A will not necessarily be a good choice for the average living/listening room when the listener is sitting 3 - 4m away from the speakers and is wanting loud listening levels and an extended bass performance.
They are a good speaker, but have gathered too much hype and mistique by the ill-informed, and because of that their second-hand value has become disproportionate. £1000 for a pair in excellent condition is probably reasonable given the close tolerance on unit-to-unit variation. But as has been said, the new Stirling Broadcast speakers are a better bet for anyone looking for an LS3/5A type speaker design (and the latter design has been approved by the BBC as an LS3/5A substitute).

