Firstly, are there any regs. about fitting such flooring in a shop?

I hope someone who knows will come along soon. I don't know. What I do
recall (from reviewing spending on public areas in a past job) is that
decisions on flooring need to take account not just of health and safety
(eg slipping, such as you mention) but also the DDA (eg is there a clear
and safe transition at the entrance for wheel chair users,
blind/partially sighted). I would have expected the Post Office and/or
the National Federation of SubPostmasters to have requirements/guidance
on this.

In the meantime dare I suggest that you jump on the risk-avoidance
bandwagon and wait to see if your client faints at the price?

--
Robin