There are two ways to look at it...

a) Compared to other cars, yes, they are not very safe. Other cars have side impact bars, airbags for and aft, crumple zones, this that and everything else. ie: The mini is not as safe as 'modern cars' because the design dates from the 1950s.

or

b) Minis are perfectly safe because millions have been sold and only a tiny tiny fraction of mini drivers ever came to grief...probably the same percentage as volvo drivers who have crashed. Therefore you are just as likely to get injured in a mini as in any other car.

I don't really think that size matters. Articulated lorries seem big whatever car you're in. The mini bodyshell is not super strong, but it is tougher than many other cars out there. Also the engine is transverse and forms a large 'buffer' at the front. Remember, that in a head on crash it is all to do with momentum. The engine is the heavy lump and once that has stopped moving the rest of the car will stop very soon after with minimal deformation, simply because the shell doesn't weigh very much. What is there up the back to squash the shell? It's only rear engined cars that tend to crush the passenger compartment. If you ask me, the mini is ok head-on in most average cases ie: hitting someone up the arse at a junction, not a 150mph closing speed smash with a juggernaut. It does lack side impact and roof protection. After that you have to think about the people inside. Probably 99% of road accident victims are killed or injured from themselves smashing into something like the windscreen or steering wheel, rather than the actual car being 'steam rollered' and crushing in on them. With this in mind, if the driver (and passenger) are strapped in securely then their chances of survival are massively increased. On my own mini I have taken no chances with safety. I have improved 4 key areas. I'm not saying this is all necessary, but may give you some ideas...

Restraint

High back bucket seats and 4 point harnesses. This ensures that I can't fly about and knock into anything. It also ensures I have adequate neck protection in the event of a rear ender (these seem more common that front enders for some reason! Maybe people under-estimate mini brakes?)

Protection from the outside world

Full roll cage with padding. Door bars, roof bars, and fixed diagonal. NO drop bracket on the steering column! This lot may seem OTT, but it means that if something hits me it is less likely to stove the car in and trap me in the mangled wreckage.

Fire protection

There is more to this that simply carrying a small 1L extinguisher loosely rattling about in the bottom of one of the side bins!!! Take this one SERIOUSLY. It's too late when you are trapped and burning. For starters those small extinguishers only discharge for about 6 seconds which is useless. Get a larger 15-20second one. Bolt it securely in front of the passenger seat (NOT the drivers seat in case it goes under the pedals). This is your method of putting fires out, but you also need to try to prevent them in the first place. Most car fires are started by electrical faults rather than fuel faults. Make sure the battery cable is in top condition and is secure. I have moved mine inside the car. Fit a battery cut-off switch! The last thing you need after a crash is sparks and boiling acid. I have moved my battery to behind the passenger seat in a special battery box. If the battery is in the boot make sure it is covered. I heard of one mini driver who had a full metal petrol can in the boot which shorted out his exposed battery terminals. Of course make sure the fuel system is sorted too. I have run stainless braided fire-proof fuel line inside, although many believe it is safer outside the car. A fuel cut off is also a good idea, although avoid having hose joints inside the car. If you are going to run fuel, battery or brake lines inside always run them along the central hump, never along the inner sills.

Accident prevention

This really relates to keeping the car in a safe condition. Make sure the tyres are good and the brakes are good. Running the brake lines internally prevents damage and corrosion. Fit high level brake light(s). Negative camber lower arms and heavy duty tie-bars help to keep the car on the road, as does stiffer suspension. Make sure all the subframe bushes are in good condition to aid handling. Fit some spotlights so you can see where you're going at night, etc etc.

Many of these modifications are beyond the scope of a standard run-about mini. One thing's for sure though, after driving around in my car I don't feel safe in 'modern cars'!!