We’d be interested to hear about similar schemes (or entirely
different ones) that reward loyalty and how they work.
For example, how long does it take to earn an extra days holiday
allowance? Is there a limit? Does such a policy have a positive effect
in your workplace, etc?
A similar scheme is very common in the US.
In almost every US company where I have worked, folks received a base number of vacation days when they joined the company. That number went up over time. (The only exceptions to this were very small startups.)
Typical would be to start at 2 or 3 weeks vacation. Then it would go up by 1 week after 5 years of service and another week after 10 years of service. Some companies had different levels. All companies had a limit. Some companies allow employees to purchase an additional week of vacation time.
All HR departments in companies where I worked subscribed to industry newsletters, studies, and networking that surveyed companies and distributed the results of their survey to subscribing companies.
This is a common thing in many locales - no need to reinvent the wheel here. If your HR department doesn't understand how this is done in your locale and/or in the US, they should probably bring in a contractor for a while to train them.