Congratulations, you have found yourself in a minefield but at least you've realised that rather than finding out the hard way.
Almost all societies of 100+ members will have become a Company Limited by Guarantee for exactly this reason. Some are also registered charities, though the benefit of this is debatable. Smaller societies rarely even think about this, and where they do it is usually dismissed as unlikely to happen and therefore not worth worrying about. As a secondary position, some take out a Directors and Officers Liability Insurance (D&O) policy, which will pay out instead of the officers being chased personally for redress. Most of the larger societies also have this, as it may make the difference between the society continuing in existence albeit with potentially higher insurance costs in future rather than being declared insolvent and folding.
Take a look at https://www.accountancywales.com/social ... -trustees/
and in particular at http://www.diycommitteeguide.org/resour ... structures
and the rest of the site around that page as it provides an excellent resource on how to structure any organisation to make sure that you have made the best effort you can to set it up in a way which doesn't come back to bite you later.
For those who think it will never happen, there are a couple of nightmare scenarios which are all too real.
The first of these is negligence by the society officers, such as agreeing to do something in contravention of your own policies - imagine your event contract, risk assessment and H&S policy say that all combat displays will be done inside a double-roped arena, provided by you, with a minimum of a 2 metre gap between the ropes to protect the audience. On arriving at the event, you discover that you forgot to load the rope into the van, so you scrounge what you can and create a single-roped arena rather than cancelling the display. Then someone in the crowd takes a sword around the head, is seriously injured, and requires 24-hour care for the next 40 years. Not surprisingly, their family want someone to pay for this, and to compensate them for the loss of earnings, so you find yourself on the wrong side of a £2-5M claim. Your insurance provider reviews the details, looks at the Facebook photos of the event, asks for all of the documentation around the society and this event, and then declines to pay out as you have been negligent. What next? The rugby club example is still valid - each officer is liable, and having taken all of their assets or a nominal amount from each of them, the members are in theory liable for the rest, although each has to be pursued in a separate case so it may not be worthwhile.
The second is more often overlooked - at a private combat training event, a new member is passed as OK to join in with everyone else after an initial training session and assessment to verify that they have reached an adequate standard. They then smack someone very hard in the head, resulting in a similar injury to that above. This time, your Public Liability insurance doesn't even come into the equation, as it offers Third Party cover only, so protects only the public. Your officers followed all of your procedures, and you have documentation showing that they have done so, but the family of your injured member don't see it that way and decide to sue the assessing officer on the basis that your procedures were inadequate and the new member clearly was not ready. Without a Member-to-Member insurance policy, you have no cover, and that one officer is fully liable. If they try to sue all of the officers on that basis that you were all responsible for making sure that the assessments and training were conducted properly, then all of the officers could be in the firing line.
Suddenly finding yourself lacking in volunteers to be officers? Not surprising - I've been there and done it in two societies, and I'd be very reluctant to do it again without D&O insurance in place, and without the society being a limited company.
Having said all of that, I am no expert - if in doubt, pay for legal advice out of the society's funds.