I have done a lot of work with Royal Mail on Health and Safety for delivery staff. The problem is not with the safety of cycling - they have relativly few accidents - it is with the weight and bulk of the post.
The current system is that the posties arrive at the office and sort the mail first into rounds and then sort the round into its delivery sequence. This is put into delivery pouches the first weighing up to 16kg and the later ones 11kg, typically a postie will have 8 - 12 pouches - around 100kg of mail each day. They can not carry all this on their backs or bikes at once so they have a safe drop system - vans wizz round dropping off bags in boxes. porches shops etc to be picked up later. Getting these drops is difficult and consumes a lot of management time - lack of these drops can lead to posties carrying over-weight pouches and contributes to their health problems. Heavy and bulky packages are also delivered by van.
Royal mails delivery operations lose money - the amount they are allowed to charge TNT, Business Post etc for the "final mile" is less than the cost of the service at present. The whole idea is to take jobs and costs out of the system - if they don't their "compeditors" will start delivering in the few areas where they can make a profit and RM lose even money.
"Compeditors" because the market is rigged to prevent ensure that they make money.
The system they are moving to is that the mail will arrive at the delivery office "walk sorted" Posties will arrive at staggered start times, feed their mail through a sequencing machine and go out in pairs in a small van. this will carry all their mail for the day. They will use the van as a mobile store as they do loops on foot to deliver, then to move to the next parking spot. The hope is that: the pouch and packet vans will no longer be needed; the posties will spend less time in the office and so either do more deliveries or less hours; the posties will no longer be tempted to overload themselves to get the job done.
Rounds close to the office will be done with trollies, some of them electric.
The latest bikes have a step through steel frame, 26 inch rear and 24 inch front wheel with marathon tyres, hub brakes and 5 speed SRAM hub gears (with a chain tensioner), rated for 16 kg front and rear carriers. I want one as a shopping bike.
) and subject to the same legislation as any office space. I'd rather leave it out but people have sued employers for tripping over cables in their own homes, so that is just the natural response from employers.
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. A reduction in cycling posties means far fewer posties out and about delivering the mail which means JOB LOSSES 
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