I don't think flow restrictions would help much - traffic would just route a different way, and you'd shift the problem elsewhere.
I think part of the problem is with the shape of airspace and sectors.
In the past, when sectors have become busy, the standard response is to reduce the size of the sectors. This is counterproductive, since the actual number of RT exchanges goes up, since you have to establish communication and hand them off, and in a small sector those become a high proportion of the workload. If you're doing that all the time and aircraft are not working you for long, then you're spending all your time saying hello and goodbye instead of actually handling the traffic, their routes and levels.
Dunno much about it except as a grateful "user", but might horizontal secorisation assist, at least, close in to London? With a ceiling of, say, FL150, so outbound/inbound traffic is limited to that as tops, and above is all the transit traffic? Outbound traffic would get further climb further out where there is less bother...
Okay, it would push fuel consumption up a bit, but at least it wouldn't mean yet more airways slots, congestion at airports and unhappy pax gagging for a chance to slot the crew!