Yes. But, what if everyone did it? 

Pebble plunderers in Cornwall warned as tourist faces £1,000 fine
Councils remind public that taking pebbles risks floods, erosion and wildlife harm
Yes. But, what if everyone did it? 
If “it” means “sex”, I’m all on board!
That Starbucks in Picadilly Circus has no idea what it’s in for.
This.
Has anyone ever actually been fined for taking a single pebble off a beach?
In the case of pebbles on the beach, I would keep a “Do Not Remove Pebbles” law on the books, but enforce it only if and when pebble removal becomes a problem. Start by posting friendly signage and if it appears the rate of pebble removal becomes problematic, post a less friendly sign, then another even less friendly sign if needed. Find the level of enforceability and signage tone that results in a sustainable pebble population.
 —please don’t remove pebbles.
 —please don’t remove pebbles.
Here in Florida we have a similar problem with people harvesting sea oats and sea grapes from beach dunes. Here is the statute (which is rigorously enforced):
 k9bfriender:
 k9bfriender:So, rather than make a limit, which would actually encourage people to take as much as they can up to that limit, even if they wouldn’t have taken any otherwise, it’s just verboten.
In other contexts, it seems to work fine to just tell people not to be unreasonable or to allow a ‘reasonable amount for personal use’. I realise that might seem like a hopelessly vague concept to some people reading this, but there are already implemented rules like this in the UK, and they work as well as anything else would.
 Filbert:
 Filbert:Has anyone ever actually been fined for taking a single pebble off a beach?
Not that I can see. But here’s something similar.
A holidaymaker who took pebbles from a Cornish beach was forced to travel hundreds of miles to return the souvenirs to avoid a hefty fine.
The man was traced to his home after taking a carrier bag full of stones from a beach at Crackington Haven near Bude.
He was told that he faced a fine of up to £1,000 so he decided to return to Cornwall’s Atlantic coast and put the round grey stones back where he found them.

Councils remind public that taking pebbles risks floods, erosion and wildlife harm
 Mangetout:
 Mangetout:OK, but that applies to a lot of things, doesn’t it? If everyone in the UK turned up at Starbucks in Picadilly Circus, all at once, it would be a huge problem, but we don’t ban people going into Starbucks on that basis.
If everyone in the country went fishing, it would be a problem, but fishing is legal. If everyone kept guinea pigs, and picked weeds from the verge to feed them, it would be a problem and the ground would soon be bare.Not everyone is going to do it, so the ‘what if everyone did it?’ argument is just spurious, isn’t it?
These are problems generally solved by economics. We don’t need to ban people from going into Starbucks because the market will correct in one of several ways - 1) Starbucks can raise their prices so fewer people just show up 2) they can increase capacity or open more stores 3) they can do nothing and let “first come first served” sort it out.
The pebble problem is an example of the “tragedy of the commons”. The beach is a shared resource so theoretically anyone can just pick up some pebbles and walk away with them.
So the “if everyone did it” argument generally applies when there are no market forces or other mechanism that would prevent everyone from just up and doing something until the resource is depleted.
There are limiting factors on the number of people likely to visit any given stretch of coast in the UK - ease of access, available parking, distance from population centres, weather, aesthetics of the beach etc. The question isn’t whether anyone theoretically can, but whether everyone practically will. They won’t.
How fast do the pebbles get replenished?
Constantly, from longshore drift, ultimately coming from erosion of cliffs way along shore somewhere. That’s basically where beaches come from in general.
So does a person picking up a pebble on the beach meaningfully contribute to depletion of the beach, leading to a greater level of erosion? Mathematically, it can’t be argued to be zero, but neither can the effect of simply walking on the beach. If you want to ban people picking up a pebble on the grounds that it contributes to coastal erosion, you have to ban people from going to the beach at all, because any disturbance to the beach - even a footprint - has a nonzero effect on erosion.