As an alternative, what about doors between the two rooms. During the day when more space is needed the activity can spill over between the rooms. At night when you want a cosy evening they can be shut. So many extensions seem to rovide no purpose for the front part of the house during most of the day and just duplicate the living space at the back while losing garden space.

Could you out the kitchen on the longer side? Kitchen feels cramped.

Is it a loadbearing wall? Do you have a floorplan of both floors? And a photo of the back exterior? Hoe deep is your garden and what direction? Are those window&slider somewhat in the current location? Do you have enough space for shoes, coats and such? And what's the depth of the kitchen, as the measurements are hard to read. So many questions ;)

Personal example: My 50s house is 'just' 6.5x6.5m plus a mudroom extension (nearly 3x3m). Would not want to live without anymore, as it houses washing machine, fridge freezer, oven (kitchen itself is 2.35m), all shoes and coats, plus keeps out the cold when entering the house. We took out the middle wall as we preferred an open plan, more light as well. My son (6) has enough space in his bedroom for a desk and when he does need help with homework, we'll sit at the dining table.

Wumi, we did at one point try the below option, but couldn't get over the problems we'd have with the stairs cutting so much into the dining area. If that wall doesn't move back, the depth of the room - it's only 2.6 metres - doesn't leave enough space for a sensible sized dining room table.

Rinked, it is a load bearing wall. The upstairs floor plan is very similar, there's an identical load bearing wall pretty much directly above. The garden's about 8 x 7 metres, but we're on a flood plain, and from the rear of the house it slopes down straight away a good 1/2 metre. So getting the foundations done for an extension won't be trivial. The existing kitchen/diner space is 5.7m by 2.6m.

Thanks all very much for thoughts, really appreciated. :)

Personal example drawing:

There used to be an enclosed kitchen and enclosed dining. We took out both walls. Our table is 150x90cm but can be extended, this would not be possible with the wall still in place. You can see why we keep our fridge in the mudroom, the kitchen is tiny, but it works for us.