Instead of restricting night flights more, why not do the opposite!
Make LHR 24/7 airport like any other leading major hubs, DXB for example.
I actually suggested exactly this directly to Sir Howard Davies during one of the AC consultation meetings. I reminded him that the noise footprints generated by contemporary airliners were tiny compared with those of their 1960's/1970's counterparts for which the night-flying restrictions were implemented. Technology has significantly reduced the decibels and increased the climb rates since then. Yet the rules still afford no recognition to these advances and the investment operators have made in re-equipping fleets with less-intrusive aircraft types. I pointed out that even if full night-flying could not be approved, relaxation of rules for compliant types would yield many additional slots which could be allocated to priority long-haul routes. And minimal new investment at LHR would be required to achieve this.
I also advised him that public perceptions of aircraft noise in the vicinity of 24/7 commercial airports is way overblown and based upon memories of aircraft types withdrawn long ago. Modern airliners don't ruin your sleep. And that is not just an expedient claim on my part. Few are better located than me to comment on such matters! ;-)
At the time, SHD replied that this was an interesting proposal which nobody had suggested to him before. He would take it away and discuss it with his team. And when the report was eventually published ... it proposed a
reduction in night-flying. So much for common sense!