I have just completed a similar side return on our period home. Looking at your plans you already have a good sized kitchen. If it were my home, I would close off the sitting room at the front and then give the 2nd part of the room to the new open plan space. Create a utility room and loo in this space - you already have the plumbing near. Then the remaining part of the dining room would become part of the new open plan space with side return. Likely you will need to move the drains - usually they are located in the side return area - this is not a big job for a competent builder. You will also need a roof light or maybe 2 to let in as much light as possible via the side return roof. We opted for 2 x 1m roof light because we also have a skylight looking into the kitchen.

Due to the layout of your house e.g. the 1st floor sits full length on the ground floor - you may need a supporting column at the end of your kitchen. We got round this with 3m bi-fold doors and then a 1.4m single pane of glass the other side of the column. Think about how you want to use the new space - we preferred to have the kitchen at the back of the room with the dining and sofa space next to the doors and looking over the garden. Also consider how you will heat the area - we installed water Underfloor Heating, it was costly but we will see a reduction in the cost of running the rest of the house, because in the winter we will spend most of the time in this area. I think it will be a great project but you are right to put in as much planning as possible before applying for planning permission etc., Once you kick off you don't want to keep changing your mind on the bigger items.

It is possible to reconfigure your room to have a new kitchen and double doors onto the garden with circa £25k but a full side return extension + new kitchen is more £50k+. For inspiration type 'side return extension' into houzz and there will be loads of images to inspire. Your budget will be key to the extent that you can do. A side return extension will pay for itself in terms of value added to the house. Good luck Ed

The configuration of the rear of your house provides an
opportunity to create a contemporary, open plan space. I would open up the side
of the house where the hob is shown and infill the outdoor space with a glazed
roof to create a large kitchen-dining area filled with light. A flat roof with skylights could be another option.

Budget permitting
you could open up the wall where the French doors are shown, or just remove
them and create a lounge/play space.