We had 16 days in Hawaii and stayed at 4 different hotels (including Aulani), and visited 3 islands. We spent 3 nights in Waikiki, 3 nights in Maui, 3 nights in Kauai, and 6 nights at Aulani. That may be too little time for some on the islands with too much moving around, but we really enjoyed it and would do it again. We decided to bookend our trip with our stays on Oahu because it was cheaper for us flying from the east coast to book roundtrip flights to and from Oahu. I have no idea what your path would be from the UK, but I imagine to fly into or out of an island other than Oahu would require you to change planes in Honolulu, rather than a direct flight from wherever you will have to layover.
I agree with PPs that if you decide to split your stay up and remain on Oahu, Waikiki is a great area to spend the rest of the time. Many hotels are cheaper than Aulani, and IMO, you can get away with not having a rental car in Waikiki which will save you on parking costs, the car itself, plus the traffic hassles. There's a lot in walking distance, there's an inexpensive trolley that goes up and down the main strip of Waikiki, and there's tons of bus tours that offer transportation to and from Waikiki hotels. We did bus tours to Diamond Head and Pearl Harbor, which worked out great. We stayed at the Waikiki Beach Marriott which was a good central location. Hilton Hawaiian Village is very popular, but its resort-like just like Aulani and its at the far end of the strip making for longer walks along the main road. We wanted something more central, and cared less about the hotel amenities since we spent most of our Waikiki time away from the hotel.
With 6 nights at Aulani, we spent every other day off-site exploring other areas like the North Shore, Kualoa Ranch and the windward side. We had a rental car during this time, which I would highly recommend. We had 2 full days at Aulani where we did not leave, plus our arrival evening, departure morning, and another 1 or 2 nights where we were back by 6pm-ish. We felt that was more than enough time to fully enjoy the resort. We also visited the Marriott up the street, as well as Monkeypod and Pizza Corner across the street. We ate at all of Aulani's restaurants and visited the spa. The luau wasn't going on at the time, but we did attend the show they had at that time. I agree with PP that Ko Olina, the area Aulani is located in, doesn't have a ton of stuff to do. Its an isolated area and its a planned, gated tourist community.