It is not a business size concern, but rather a shipment size.
You can use any of UPS, DHL, or FedEx. The fees will vary with the size of the shipment.
I don’t recommend small shipments at all unless they are valuable, since the shipping costs may end up as a high percentage of your cost and that could prevent your items from being competitive. If you have existing account, you may get a better deal. Otherwise, you may want to include that with your negotiation to set up the account. If you are planning to make a serious business of this, you should be planning on a substantial amount of sales to cover the costs of operating the business internationally. Unless you are able to use local suppliers (in the UK) you will need to set up at everything you plan to sell. If you don’t ship much, you will run out of stock well before you can restock. For example, if you plan to sell 100K, you will need at least 50K in stock and with the shipping costs involved, you may be in a better position to negotiate.
I prefer to deal with larger shipments so that the cost is under 10% of the value of the shipment so that I can still sell competitively. That would require more shopping around.