I've been to Hawaii, but travelled from the US, not U.K. the people I know who have been from the U.K have broken their trip on the west coast of the US, due to the travelling times.
Hawaii is beautiful and well worth a visit, but I think you need to combine the islands to make it worthwhile (which is easy to do as you have three weeks!). Flying between the islands is like getting on a bus or train in the U.K.
Have been to Oahu, the Big Island and Maui.
We went to the Big Island specifically for the Volcano, there's a National Park there. In fact, the Hawaiian islands have a number of national parks, so if that's something you're interested in, you should investigate the cost of an annual pass v day entry to every park.
Volcano National Park is on the opposite side of the Island to the main resort area, and it takes a while to drive between the two, so something to be considered although the capital, Hilo is very close and you could stay there for a day or two.
When we went to Oahu, we stayed up on the North Shore rather than down in the Honolulu/Waikiki area as it's really busy down there. We explored a lot all over the island, there's plenty to do, lots of hiking, the Polynesian Cultural Center, shopping in Honolulu, visiting pineapple plantations!
Maui was just a single trip, we looked at combining it with Kauai but in the end couldn't be bothered flying around.
Maui is much quieter than Oahu, there's a beautiful National Park where you can watch the sunrise over the mountains (although that is extremely popular and to get in you have to get up stupendously early). Some nice quiet towns and lovely drives.
I would say that you could do a once and done holiday of a lifetime to the Islands in three weeks and have a really good time, but if you just went to one, you'd be bored in that amount of time.
Food is really expensive there, something to factor in if you were planning to self-cater. There are Costco stores in places, so if you have a card you could use it to stock up on some stuff (like the legendary rotisserie chicken or pizza slices!)
Oh, and don't forget how close to the equator it is, so daylight is pretty much 6am to 6pm, it gets dark really early and it's useful to have a torch or headlamps for if you're out after dark.