Hi Arcticklein. Really hope you had a good time in Great Douk. Many cavers will cite this as one of their earliest trips, and some will have then gone on to have caving as a lifelong passion!
A few useful resources for you...
Some advice on how to stay safe in the caves of our regions. Research, weather and knowing the capabilities of your group.
Specifically in response to your question... always two totally independent, robust, fully charged, and for a wet cave, waterproof light sources, ideally one being helmet mounted. Robustness and redundancy is key. Also take note of the advice in the above link regarding setting a callout just in case the worst happens.
Most of the caves and potholes in the North of England have SSSI (Site of Special Scientific Interest) status, either for botanical, biological or geological interests. These sites are vulnerable and need to be protected and conserved.
Other useful advice to help get you more involved in caving, including a list of clubs who accept less-experienced new members (a club is an excellent way to get involved in caving, although we know lots of people cave outside of clubs too):
Caves are a fascinating part of the great outdoors and their exploration is full of adventure. As with many activities there are risks. Good preparation and learning from the experience of others is key to caving safely.
Plus loads of cave access information, route descriptions and other advice on our website, covering caving in northern England and Scotland. If you haven't already see the following document for Great Douk:
Access information and route description for Great Douk Cave (Chapel-le-Dale)
Hope this helps!