I would take the whole wall out and put new kitchen in maybe with peninsula. You could possibly extend right way and put a small side return in to fit a utility and toilet near existing kitchen. It depends on budget I suppose.

Would you move the toilet ?

It’s hard to envisage what difference that would make on your plan in terms of space provided. You could put under the stairs but would depend where soil stack is. For now until you know whether you are extending fully and doing a job from scratch, I would leave it where it is.

It's hard to come up with solutions if you don't know what the problem is.

Except that you'd like "a bigger kitchen area", you haven't really articulated exactly what your issues are.

How long have you been living there? You should always live somewhere for 6-12 months before defining the problem.

Is it kitchen storage or kitchen worktops that you need more of? If you had a utility room, would moving the appliances and freezer out of the kitchen give you the extra space needed. There are lots of simple solutions there.

You mention adding a family room in future. Would this be on just one side or full length of house?
Maybe consider this as you decide where to place kitchen, so you get the best use of space now and in future.

One side you would still have good sized garden but full length, depending on how far you extend out, could make garden less appealing if you come to sell in future, as your garden is very wide, but not very deep.

If you decide your final layout first then you might be able to get there in stages to reap some of the benefits early. I had a similar layout and part of my extension was to the side of the old kitchen, giving me a 1.3m wide utility room which is sufficient to hide a lot of mess. The full extension follows the line of the utility back about 7m and across 4m and is open to the old kitchen and old dining room. Apart from the wall of the utility being load bearing for a steel, it could have been done independently of the back extension. A side extension could house your cloakroom too.

The garden is about 100ft long. Ideally the family room would be the full length of the the house. Utility room would consist of washing machine, dryer and hoover, mop etc. Lived here for 6m now. Main issues are: 1) do we save the main kitchen for the extension which could be in ,5 years. This would run parrell vertically to the dining area or knock down the wall and do a kitchen diner now then when we extend it would make another family area 2) the hallway is narrow and there is nowhere to store shoes and coats due to toilet area. Thinking whether to move this under the stairs now to give us more space 3) utility area when we extend could go where the kitchen is (some of it) or at the side depending on£££

I would suggest for now, turn the kitchen into a utility and put a door through from the dining, then add a cheap and cheerful kitchen into your new kitchen diner making a good size family space. Then when you add an extension this can be open-plan to the kitchen and just be a large dining / living area without the need for plumbing, etc.

I would leave the loo for now personally. Seems a lot of extra cost for little gain.