I would turn the island through 90degrees and attach it to the wall. Move your dining table to the living area and open up the kids room as a general sitting room space - all open plan. You should also consider the aspect of the space as this would greatly influence the layout you decide on - where is the sun morning, midday, evening?

In the main I agree with Patricia.
I would move the dining table to the living area, move the living area to the kids room, move the island a little more to the right so it is just a little more over than the width of the entrance walkway, at the moment it is more to the left and almost interrupts the entry flow enough to keep catching your self on the edge, with the table moved it will allow this, plus there may be enough room for more storage on the right hand wall decorative or practical and naturally shallower than standard depth, consider what it would be used for then you can make an informed decision on depth. The island sink and bin are not far from the tall unit pantry and fridge, so no I don't think they are to far away, whatever you get from these places are to be opened probably by the sink or bin, or opened to eat from the packaging.
Also why would you have a log burner and an aga in the same room unless your aga is an electric one? They both give of tremendous heat, an aga is constant and unless you have planned for other oven types it will be year round so summer as well, as Patricia mentioned bare in mind how the sun transits your house, where it's position is when you will be in these areas which I'm guessing will be most of the time.
I know plenty of people who gave had " improvements revamps etc" to their kitchen dining living spaces with plenty of regrets, loads of glass to bring the outside in, underfloor heating and an aga, the underfloor heating is switched off you can't zone it to where you want it, and the aga gives of to much heat with the glass combined, all the hard surfaces, no acoustics were considered by the so called "architects" sound is a problem too, something else to consider, someone else had to have some of their new kitchen change to make room for an air conditioning unit because of the heat, this is very expensive to run constantly, summers are almost unbearable, these things also affect materials being used such as leather and wood drying out and cracking/splitting.

I hope this has been helpful.
Kind regards
Barbara

Hi Natasha, sorry I also meant to suggest if there was room you could extend the worktop over gang on the right side of the island to allow for leg room so seating could all be on that side, as it is it looks a bit squished, this is viable with the table moved.

Kind regards
Barbara

Think about where in the extension you will want plenty of natural light and that will help you decide where the kitchen area needs to be. Then, in what part of the room will you especially enjoy a connection with the garden? If you prioritise these issues then the rest should fit in around them and the layout will be successful. Jane