My 1970's Roy Thame (same builder/workshop as Holdsworth professionals etc) uses this bolt

- Roy Thame binder bolt from 1975
Which is;
- threaded 5/16" x 22tpi (5/16" BSF)
- is full-threaded
- has a threaded length of 3/4" (19mm)
- has a head diameter of about 7/16" (~ 11mm)
- has a head depth of 5/16" (~8mm)
- uses a hex key size 7/32" (~5.5mm)
It is in all respects a bog-standard 5/16" BSF caphead screw, in high tensile grade (equivalent to modern 12.9 grade).
The core size of the thread is about 6.8mm, so measuring the ID of a hole tapped 5/16" BSF is likely to give a measurement around 7.0mm. However this won't help distinguish it unequivocally from a number of other screw threads.
Standard BSF caphead screws have a smaller head diameter in relation to the shank than metric capheads; this makes them an inherently better choice for this application, because the bolt is loaded in bending as well as tension; it doesn't need a big head as a bolt loaded in pure tension might.
5/15" whitworth is also used in some old seat binders and the external head size of a caphead screw is the same for a 5/16" whitworth caphead as for 5/16" BSF, so no clues there. In theory the core size of the whitworth thread ought to be smaller but in practice it might not be.
To identify the thread pitch a set of thread pitch gauges can be used. Alternatively IME a standard M8x1.25 threaded bolt will enter a 5/16" BSF or a 5/16" Whitworth hole and go in a turn or two before it starts to bind; this doesn't much help you distinguish between the Whitworth (18tpi) thread and the BSF (22tpi) thread; 1.25mm pitch is very close to 20tpi, so they are both about equally wrong.
It is tempting to tap the fitting to M8x1.25 but the resultant female thread won't be very good and a M8 bolt head will have to be machined to fit the seat lug; it will be too fat otherwise. I does avoid having to carry an odd allen key for that bolt only though, since a 6mm key will then fit.
cheers