There have been plenty of suggestions in this thread of things that would 'improve the situations', but I have been commenting on why I think these will not happen, or not happen quickly, mostly for logistical and/or [ultimately] economic reasons. Much as these reasons annoy UK (and other foreign) contributors but, unless the basic laws, rules and practices of economics are suspended, they are likely to remain.
I have no idea why the 6h16 from London does not call at Lille - every other Brussels/Amsterdam train in both directions appear to. Maybe there is a good reason (platform occupancy at that very time it passes possibly?) Perhaps write to E* and ask them? However, it seems that this would only offer one additional connection over the following 7h04 London-Brussels train. I have just had a look at the E* website, and the SNCF Voyageurs website, and see that seamless through booking appears to be offered between London and Lyon or Strasbourg (for instance - various other provincial French stations seem to be available) changing at Lille.
All the countries in Europe would benefit passengers by having a unified ticket booking system, however the financial implications of that in regard to missed connections etc and the sheer cost of development mean that this is unlikely in the short to medium term.
However much train enthusiasts might like to believe, France does not have the same demographics, geography, economy and politics as Germany or the Netherlands or Austria. The demand profile is just not the same, with the presence of an all encompassing mega city of Paris (the likes of which are in none of those countries) and such a huge area of thinly populated countryside. To the people outside, a German style timetable system is just obvious, but I don't think it is at all as simple as that from an economic point of view. As for blaming the current service on some sort of conspiracy of the French political class, just laughable even if there is a grain of truth in that all political systems favour the status quo.
So far, the main solutions proposed have been to force the French Government to: find billions to end cross subsidisation between Intercity/International services and other activities; run services at unlikely marginal rates, requiring additional trains and staff, which are to mainly benefit long distance foreign passengers; introduce more frequent long distance regional services requiring extra trains and staff with uncertain financial result; introduce clock face timetables on main lines flattening peaks of travel to and from the mega-city (presumably with resultant overcrowding) or requiring additional trains and staff to cope with the peak, again with uncertain financial result. All in a country which has well known financial issues facing it funding social care/pensions.