You are right to worry about the heat from the sun, it can be a killer, the approach you have taken is a good one but, there is always a but, while your proposal maybe sound if you live in London there are many places in the UK where such a set up will be too cold in the winter.
You need to work out the heat loss for your location, I would guess that you have not allowed for the sort of losses you can have on a cold winters, or summers day, for that matter. Taking that door away may lead to a freezing home.
If you are facing true South, or thereabouts, the sun will not get round to shining in the conservatory until elevenish, leaving you will a cold breakfast room. If on the other hand if you have a three aspect room it will get very hot, very quickly and while your proposal will clear the heat on a windy day, on a still day you will boil.