Hawaiian Airlines simply doesn't have any aircraft that can operate the flight.
For now, Hawaiian Airlines does not consider its A330-200s to have sufficient range to reach London with the desired payloads and it's not yet sure whether its upcoming A330neos will be able to, either.
Flights to London are a goal but may be at the limit of what’s attainable after the carrier swapped its order for Airbus Group SE A350-800 jets to the shorter-range A330neo in 2014, Hawaiian Holdings Inc. CEO Mark Dunkerley said in an interview Wednesday.
“We certainly hope the answer is yes but we don’t have all the information we need,” he said. “It’s going to depend on what our final seating configuration is and therefore the weight of the Neo and its exact performance and statistics when it’s actually built.”
Source: Recent Bloomberg article citing Hawaiian's CEO
Note from the above quote that Hawaiian has replaced the A350 order mentioned in another answer with an order for A330neos instead, so it currently has no A350s on order.
One interesting note from that same interview is that Hawaiian is also looking at possibly acquiring some of the cheap A380s currently floating around on the market. However, it's considering these for its current high-demand markets such as Los Angeles, Las Vegas, and Tokyo, not expansion to Europe.
Dunkerley, 52, said the airline is looking seriously at whether the Airbus A380 might have a role to play within its network, especially on routes such as those from Honolulu to Los Angeles, Tokyo and Las Vegas, which it serves with smaller wide-body planes six, three and two times daily respectively.
The argument for using the superjumbo, which might be available on attractive terms either from Airbus or, soon, in the second-hand market, isn’t conclusive and Hawaiian needs convincing of the business case, Dunkerley said.
The main problem overall with direct flights between Europe and Hawaii (on any airline) is what Zach mentioned in his answer: It's an ultra-long-haul leisure route.
It's very hard to make the numbers work for such a route, as airlines typically rely on selling expensive close-in-booking and premium-cabin tickets to business travelers as well as relying on them to keep load factors up in order to turn a profit for their ultra-long-haul routes. This route would also be competing with several existing single-stop routes with connections in New York, Chicago, Atlanta, Denver, Los Angeles, Seattle, etc. These routes are already economically feasible due to the much higher demand for traffic to London from these connecting points (and other cities feeding to them) than from Hawaii. Similarly, demand from the U.S. mainland to Hawaii is much higher than from Europe to Hawaii, so those existing flights remain viable.
With that said, there are recent rumors regarding the Swiss leisure-route-focused airline Edelweiss possibly starting a route to Hawaii from Zurich soon using A340-300s, but this is presently still unconfirmed. The economics of this seem pretty sketchy, though, and the "as early as December 2016" start date mentioned seems even more sketchy.