Sidelevers were the opening method of choice for Stephen Grant, Boss & Co (pre-Robertson), Blanch and a few others until the toplever won the argument and the public voted with their thumbs.
Grant produced a shed load of sidelever, hammerless ejectors let alone their hammerguns; Boss a few hammerless but mainly hammerguns; Blanch very few hammerless but most of their quality, in-house hammerguns.
I once went out on a limb and said that if a Blanch hammergun had a top lever, it was bought in finished from the trade but now I would be rather less dogmatic!
Most other Makers produced a few sidelevers in both hammer- and hammerless: I have sold two H&H 1st model Royals SLE's with them but they are nowhere so prevalent as the usual suspects above. I haven't to date ever seen a Purdey Beesley S/O action with an ORIGINAL sidelever but never say never!
With all due respect to Argo44, the patent that MOST of the quality sidelevers are built on is the Purdey so-called Thumblever patent 2nd type. This describes the spring that is fixed at the rear of the triggerplate, passes round the triggerbox on both sides and meets again just behind the upper end of the lever, linked to it with a swivel in most cases. The sidelever is to all intents the same as the thumblever but passes round to the side of the action instead of lying in the gap of the triggerguard.
The photo that you show is most likely a rather simpler mechanism mainly used by the lower end of the market which uses a simple flat spring lying under the lumps in the base of the action and operating on a lip on the front of the lever boss.
Nothing wrong with this mechanism but it is not in the same league as the Purdey designed version.
As to the usability of a left/right sidelever: I love shooting my sidelevers which are all right side. But I am a south-paw and find the RH version falls naturally to my 'young' (I wish!) left hand thumb.
Someone above mentioned the Grant lever cocking sidelever actions. These, along with the Lang patented versions, I find quite difficult to regulate for ease of use and once done require a thumb of spectacular strength to operate when both barrels have been fired.
Although not uncommon and naturally finished as Best guns should be, they were not a successful venture and only appear to have been made for a short period before barrel cocking took the trade by storm.
Perhaps the best side-cocking design, certainly the most successful in terms of sales, was the Gibbs & Pitt which was also available as a Daw's and top-lever. I have even seen an example retailed by Purdey.
