Why aren't there direct flights connecting Honolulu, Hawaii and London, UK?
Simply, because no airline has determined the route makes economic sense. 

A poll doesn't necessarily translate into a ready market of passengers. Sure, lots of people might check a box on a survey saying they'd like to see such a thing, but does that really translate to thousands of people actually a significant sum of money for the service? Would enough of them travel frequently enough at a high-enough price point to make the service worthwhile? There's no guarantee of "certain profit," and considerable money could be lost investing in such a route if it turns out not to be a success. A few reasons why it might not be a slam dunk:


Some passengers already travel between London and Hawaii, through connecting flights. A non-stop flight might cause more people to fly this route, but it would also cannibalize existing business from the connecting flights, meaning you'd need to get further customers to make up the difference. 
LHR-HNL is about 7,200 miles. As you note, this should be within the capabilities of long-range aircraft, but we'd still be talking about a flight on the order of 16 hours. This is quite the distance. Would enough passengers want to travel this long between the cities? To put it another way, are passengers willing to travel that long also willing to endure a bit longer of a journey by making it a connecting flight?
The airline operating the route needs aircraft capable of such long flights. If they don't already operate a suitable aircraft, they need to acquire some and train pilots and mechanics and ground staff, an operation that takes years and hundreds of millions of dollars. 
Hawaii is generally considered a leisure destination, and it's generally a fairly expensive one at that. Londoners have access to lots of rather inexpensive flights on low-cost-carriers to beach resorts within at most a few hours flying time. Many are in low cost of living countries where accommodation is fairly cheap. Tenerife, Greece, Southern Spain, Mallorca, Cyprus, and a number of Eastern European destinations are all rather accessible, and operators frequently offer packaged trips. Such destinations may not be exactly the same as all the splendor of Hawaii, but they're much cheaper and don't require 16 hour flights to get there. 
Will the route be popular with business travelers? Keeping such a service profitable is far easier if you have a regular stream of business travelers between the two cities, especially if they're willing to pay for premium cabins and last-minute bookings. Ultra-longhaul flights without a large supply of business travelers just don't work.
Landing slots at Heathrow, the most logical place for such a flight due to its connections, are in very short supply and thus quite valuable. This further increases costs. 
Ultra-longhaul flights work best when they're connected with an extensive route network, so they can receive feeder passengers from and carry passengers to other connecting flights. That's why they generally serve major airline hubs. Honolulu, because of its location, isn't an ideal high-density hub. Its main links are to other Hawaiian and Pacific islands, along with the US West Coast and East Asia, generally to cities that are already served by direct flights to London. As such, adding such a flight would not be that useful in helping an airline build its network. In addition, if Hawaiian were to operate the route, it would need to develop partnerships with European airlines to build a route network there (so as to facilitate booking, of say, HNL-LHR-CDG), a process that could involve lengthy and expensive negotiations. 
Is there significant air cargo demand? A very profitable cargo route may help make up for lower passenger demand, but is there a lot of demand to ship cargo between the two cities? The amount of cargo payload you can take also depends on the aircraft you choose. Some aircraft do have the range to make the flight, but would have payload restrictions, which reduces profitability. Larger aircraft may have more capacity, but may be harder to fill.


Also, according to this forum post, a service was operated in the early 80s (with a fuel stop), and it was rather unpopular and thus unprofitable.

All that said, ultimately, all we can do is speculate. Airlines study potential routes extensively, but they don't release their internal numbers. If one thought it made economic sense, they would introduce the new service.