Simon,
I'm sure you found the answers to your questions two years on (!) but for the benefit of anyone who is interested...
Swords
It is important to distinguish between the ‘operational’ swords issued to the Met in its early years for riot control and the largely ceremonial swords carried by Inspectors and above from the latter part of the 19th century. Before the introduction of the latter it is likely that the operational swords would have been used for ceremonial purposes… however it should be noted that this is probably restricted to formal photographs and the like because what we now consider as ‘cermonial’ (such as Guardsmen on duty at Buckingham Palace or policemen in tunics on Trooping the Colour) would not have been ‘ceremonial’ but an actual, operational duty in the latter part of the 19th century.
In the photo on the following link the Superintendent (erroneously described as an Inspector) is mounted, wearing ceremonial dress. The sword he is carrying is the 1822 Light Cavalry / Royal Artillery Officers' pattern sword. In all photographs I have seen of senior ranks with swords in a similar era it is always of this pattern. The earlier styles of sword depicted by the OP at the top of this thread are more of an 'operational' sword for actual riot control rather than ceremonial use. I can only surmise the reason for the 1822 pattern sword being chosen is the close resemblance it bears to the MP issue sword with barred hand guard. It could also be because its selection by the Met was before the introduction of any of the current army issue swords (1897 infantry, 1908/12 cavalry swords, etc)
Superintendent in full dress with sword: http://www.pmcc-club.co.uk/museum/displayimage.php?album=201&pos=137
The mameluke carried by the Commissioner in the link you posted is the same as that carried by Generals and Field Marshals in the army. That said, I have seen recent photographs of Sir Bernard HH carrying what appears to be the 1822 pattern on his horse. Bearing in mind this man made up his own rules and wore a PCs tunic instead of the ACPO-pattern one because he “doesn't like belted tunics”, it wouldn't surprise me that he is just carrying any sword he could obtain to “look the part”. Though the City of London Commissioner is also now carrying the 1822 pattern sword so maybe it is to prevent the unnecessary expenditure of a mameluke.
It would appear the following was the case with the MPS:
Constables and Sergeants do not carry swords, being as they do not hold equivalent “officer rank”. Obviously this rule does not apply to 'operational' swords.
Inspectors and Superintendents traditionally carried ceremonial swords (hence the sword slings worn in full dress until the 1970s to indicate such rank), which would be of the 1822 pattern. This rule would be similar to all Commissioned Officers in the army who carry their regimental pattern swords below General rank.
The Police Commissioning ranks above Superintendent carried Mamelukes in recognition of their equivalence to General Officers in the army.
(In this description I have left out Chief Inspector/Superintendent because they did not originally exist and even to this day legislation giving powers to certain ranks only refers to PC/Sgt/Insp/Supt/Chief Officer rank)
To further complicate matters, I recently visited the Met museum at West Brompton and on asking about swords was shown the earlier style ‘operational’ swords and an 1897 pattern infantry officers’ sword. The 1897 sword featured military markings so I strongly suspect that IF this was carried by a Met Officer that it was carried over from previous military service or was an heirloom. There are no MPS markings on it. It is therefore possible that if you see photographs of Inspectors / Superintendents with other types of swords that they either have military background or are just carrying anything they could get their hands on!
Sword belts / knots
The sword knots in the photo of the Supt are black leather. The belt worn by a Superintendent would have been underneath the jacket, almost identical to a current officers of The Rifles regiment.
Inspectors wore a patent leather version of the leather belt worn by PCs and Sgts (with snake clasp) over the tunic with the slings clipped together. Knots would also be black leather. The same website of the link I have posted shows an Inspectors dress uniform with sword belt, although incorrectly clipped over the shoulder like a sam browne. The carrying of swords by Insps/Supts was discontinued in the 19th century but the wearing of sword slings to denote officer-rank continued into the 1970s.
Inspector wearing full dress: http://www.scottishpolicemedals.co.uk/s/cc_images/cache_2441005270.jpg?t=1389482984
Constables and Sergeants have never been issued with 'ceremonial' sword belts, only a black leather belt with snake clasp. When swords were carried they had a sword frog similar to those worn by infantry soldiers in the army as depicted in the May drawing above.
Chief Officer ranks traditionally (individual flair notwithstanding) wore silver and blue sword knots. This would be worn on an underbelt (like Supts), and a blue/silver waist sash. On events like QBP this is still worn over the full dress tunic and with riding breeches with silver oak leaf stripe, and cocked hat. Horse cloak in inclement weather.
The sash is often still worn without sword by the Commissioner-ranks for dismounted ceremonial events. On such occasions the trousers have a silver oak-leaf stripe down the side. The open-necked tunic, peaked cap and white gloves are worn.
Last Met Commissioner in full dress - mounted: https://ssl.c.photoshelter.com/img-get2/I0000s8ujtn21vcI/fit=1000x750/People-010.jpg
Met Commissioner in full dress - dismounted: http://www.gettyimages.co.uk/event/royals-attend-met-police-memorial-service-53155260?esource=SEO_GIS_CDN_Redirect#prince-charles-prince-of-wales-sir-ian-blair-and-camilla-duchess-of-picture-id53165501 (this is Sir Ian Blair - Bernie HH never wore the correct tunic and Sir Paul Stephenson was never around long enough to attend a formal parade!!)