You are correct, you can have the car serviced outside of the dealer network and maintain its manufacturer warranty. But the garage will need to service the car in accordance with BMW's service schedule and use approved parts and fluids (and show this on an itemised invoice).

If you do service the car outside of the BMW dealer network you will save money. But the car may miss out on important updates and software upgrades (which are usually applied by the dealer at the annual service). BMW UK and the dealer will also be less inclined to provide free assistance with any issues that may arise outside of the manufacturer warranty period, too.