Is there any regulation on what surface should be beneath a fire door? Does it have to be a hard solid surface or is carpet allowed?

There is no regulation on what surface should be beneath a fire door and carpet would be allowed. However if there is a carpet joint under the door, it is particularly liable to wear and tear in places below the door where a threshold plate can cover the join to prevent both wear and tripping hazard.

Or if your floor surface is particularly liable to wear and tear in places below the door (eg, a high level of traffic, or over a carpet that may become compressed over time), then a threshold plate will help to prevent these uneven areas affecting the threshold sealing.