How are barometric pressure measurements traceable over centuries to 100 parts per million accuracy? The BBC News item Barometric pressure in London 'highest in 300 years' at least begins with

Overnight, Sunday into Monday, London's Heathrow Airport recorded a barometric pressure of 1,049.6 millibars (mbar).
It's very likely the highest pressure ever recorded in London, with records dating back to 1692.

It links to this Met Office tweet

So far Mumbles Head in Wales appears to have recorded the highest pressure during this current settled spell, with 1050.5 hPa earlier this evening. This remains a little short of the 1050.9 hPa recorded at Benbecula 16.1.1957, and the UK record of 1053.6 hPa, Aberdeen 31.1.1902

and then continues:

Met Office hourly observation reports recorded 1050.3 mbar at Liscombe in Devon, at 2100 GMT on Sunday evening. 1,050.2 mbar was recorded at Dunkeswell in Devon, and 1,050.5 mbar at Mumbles, in South Wales, shortly after.
None of these measurements breach the 1,053.6 mbar recorded at Aberdeen Observatory at 2200 GMT on 31 January 1902, which remains the national record, but the events of the past 24 hours certainly marked the first time for over 60 years that 1,050 mbar has been attained anywhere in the British Isles, said Mr Burt.

To discuss these records it is necessary to compare barometric pressure measurements to 0.1 mbar accuracy out of 1000 mbar, which is at the 100 parts-per-million level.
Question: How are barometric pressure measurements traceable over centuries to 100 parts per million accuracy? What was the procedure used to calibrate barometric pressure centuries ago that could be reproduced and compared to today's standards, or is there a very old standard absolute barometer somewhere that is believed to have remained calibrated?
Mark's answer about mercury barometers is correct - but it is not the complete story.

Barometers were initially constructed using water, not mercury, on the manometer principle.  Water is lighter than mercury, so a water barometer requires a 10.3m tube.  1mbar is therefore roughly 1cm, and 0.1mbar measurement is clearly trivial using a ruler with 1mm gradations.  Of course the exact units of measurement would depend on the country in which the measurements were taken, but it should be clear that measurement to this precision was perfectly possible, albeit with an inconveniently-large barometer!

Mercury barometers, with around 75cm height of mercury at 1bar, were significantly more convenient.  As Mark says, this does require a much more accurate ruler to measure it though.

But the accuracy of a simple ruler is not the complete story either.  The Vernier scale was invented (or at least popularised) around the same time.  With a floating Vernier marker, mercury barometers could be read accurately to around 1/10th of the ruler scale.  For a ruler marked in 1mm intervals, a 75cm column of mercury could therefore be read to 133ppm accuracy, which is close enough in accuracy to the original water-based barometers.