Free route over the London FIR will come in. NATS are working on it. It'll probably be FL310+.
The problems with redesigning the London FIR are
1. There is limited space because of the closeness of the airports in and around London.
2. The amount of traffic that wants to go south and east from London and the same with overflights
3. No matter how well you design SIDs and Stars that theoretically miss each other IF the aircraft flies them exactly you will end up with some traffic being penalised at the expense of others (that's a big if...)
4. You can redesign the airspace around London as much as you want, take the traffic from one place to another, change this route and this route etc etc but you've still got to connect it to Europe which is not going to redesign their airspace to suit the UKs fancy plan...
5. The military