Whilst a stick is not the best way to get a company to buy into H&S it can still be a part of the solution. Your best place to look is the press releases on the HSE news page. These contain recent fines handed out to companies for various infringements.

For example https://press.hse.gov.uk/2019/11/12/places-for-people-homes-fined-after-five-employees-developed-hand-arm-vibration-syndrome-havs/ Shows another company being fined for ignoring vibration hazards. If I am not mistaken it is also around the level a £4m turnover company would be fined. I think it is up to £1.6m for a company with a turnover of between £2m and £10m.

As always there are experts on here that now a lot more than me though

Of the three things you've mentioned, the lack of monitoring for RPE and vibration aren't likely to incur a fine generally speaking (unless they lead to occupational health issues of course), and are more likely to result in fee for intervention costs whilst the company is forced to introduce them following an inspection.

The "biggie" however is the work at height issue.  You state "work at height accidents", but in fact there doesn't have to be an accident to incur a large fine for breaches of the Regulations, simply putting someone at risk is enough to trigger punishment.  The size of any fines would be dependent upon the size of the company and its profits/turnover and level of culpability (as with all H&S related fines these days), and could range from several thousand pounds for a very small company, to millions for a very large one.  Either way, not worth the risk of ignoring work at height risks and regs.

Well to be realistic due to cuts etc the HSE tend to be reactive for most employers (except construction where they are still trying to be proactive). Assuming something goes wrong (a RIDDOR or a claim is made that they become aware of)  they turn up and give advice, so if you are not carrying out  face fit testing they will send you a letter saying what you are not doing right and telling you what you should do. This is not an improvement notice (which can be challenged) but a fee for invention thing- cost £200?

If the HSE come back in 3 months’ time and there is no evidence that anything has been done about the issue then the will start with the improvement notices and start looking at prosecutions.

Of course, if the original incident reported is serious enough then they start throwing notices (including prohibition) and prosecutions into the mix straight away but this is rare.  If someone gets sent to court they usually thoroughly deserve it and have often been given several chances to sort themselves out.

Re-reading the original post, it looks as if your clients are trying to balance the cost of legal action ie potential fines against the cost of proper compliance. If that is the case there is something wrong with the culture, I’d say.

Shut up shop - the HSE has been challenged to establish a "Building Police Force" which will mean more construction site visits (initially) to monitor standards

https://www.constructionenquirer.com/2020/01/20/building-safety-police-force-to-be-run-by-hse/

This client you are asking about unless they get their house in order through confetti (sorry FFI)

Originally Posted by: Roundtuit

Shut up shop - the HSE has been challenged to establish a "Building Police Force" which will mean more construction site visits (initially) to monitor standards

https://www.constructionenquirer.com/2020/01/20/building-safety-police-force-to-be-run-by-hse/

So what will this “new” force do?

Enforce existing regs including CDM?

Will it take over Building regs enforcement from the local councils and fire safety from fire authorities?

Will the have a snazzy hi-profile uniform which they can parade in front of the media?

Will it be run an outsourcing company who are paid by the number of prosecutions they achieve rather than the hopeless Civil Service who of course know nothing about Health and Safety?

Will it be expected to be self-financing at no cost to the treasury?

Will Boris answer this or any other question?

Don’t hold your breath.  

Be cautious about quoting a company/ incident/ penalty.  Those that look impressive are often appealed and reduced shortly after the news headlines, they often only come to court after protracted time period ( years rather than months) and quite often you can find similar incident with relative low penalties because of various circumstances that are not shown in the headlines.  
perhaps instead of the fine, look at a court case and use the fact that throughout the time to trial, the company is already penalised through prep work, bracing for the fine, dealing with the insurers, haggling by contractors past, present and future etc.  If they are working at max capacity now, how will they function whilst all that is going on... the hassle factor could really disrupt their business plans.