Tax and duty have two purposes: raising revenue and modifying behaviour. If you can find a tax that does both simultaneously, that's probably a good thing for policy, but long-term it may be bad for revenue. The UK is unusual in that it doesn't tax the offshoring of profits very much, in comparison with other European countries. They don't do it directly, but they do have a much higher overall cost of doing business, for example in very restrictive employment law or other, more direct costs, in local community taxes or energy tax, etc.
This doesn't inhibit large companies much in the way they operate. You *do* see an effect in manufacturing, where absorption costing makes it very obvious wherever businesses operate in high-cost locations, but generally, other types of business set up wherever they can turn a profit. Overall, in other EU countries the higher tax regimes don't stop multinats from selling there. And if you want manufacturing, you can do what Ireland has done and relieve the taxes for preferred activities.
In any retail-focused activity, the objective *always* with multinationals is to achieve monopoly market share (around 40%), at which point they can dictate terms, to both customers and competitors and the free market rules break down. This is what supermarkets aim to do - if you're the biggest shop in a small town, you can charge what you like as your customers have nowhere else to go. Supermarkets, coffee shop chains, fast food chains, telecoms, bus companies, and so on are all highly competitive until they win, at which point they're protectionist and greedy. They don't compete on a level playing field with the smaller fry, as they have more corporate resources and economies of scale.
You mention EU rules, and I think you're right: One effect of the EU is to make life easy for multinats, who "lobby" legislators to get what they want. They have the resources to do this, and they thrive in a highly-bureaucratized environment because bureaucracy tends to result in fixed costs (overheads). Big companies can easily comply whereas the cost for smaller competitors is usually disproportionately high. Driving down variable costs usually doesn't help much.
Apparently pike (esox lucius) can grow to an as-yet unknown large size. The largest yet caught was around six feet long and around 80lb, but scientists think the only limiting factor is the size of the lake and the food supply. In Loch Lomond, for example, there are persistent rumours of something around eight feet long that takes large wildfowl (pike are known to drown ducks). Pike are cannibalistic, and can drive other fish species into local extinction, as they are very efficient predators. Some pike lakes have ended up full of fish, though mainly pike!
I firmly believe in a diverse economy, with businesses of a range of size, and business activity. Not having that makes an economy (and a nation) vulnerable, as we've recently found with our "service" economy - the buzz phrase of only a decade ago.
I think the same growth rules controlling the size of pike can be applied to large corporations too. For the health of the other 'fish' and the environment as a whole there needs to be fish management!
E.