This wall is the original outside wall of the building and it can be removed but will require steels to hold up the wall above it. Everything is possible but this is the second time you have posted the same dilemma in a month suggesting you need help beyond this forum. Firstly consider your available budget- this house will likely require £50k worth of upgrades like kitchens, bathrooms, flooring, decorating, window treatments, lighting etc etc. So to consider building work such as raising the dormer at the side, knocking down walls and reconfiguring the interior you will need tens of thousands more (this is mentioned as I don’t believe you have stated your budget). My next step would be to an architect with a structural engineer friend- you need to be realistic about what you can and can’t alter within your budget. The architect will help you realise what you need the house to do, what planners are likely to say and give you sound advice about layout including help to realise how big the front bedroom would be if you squeeze an ensuite into it, the implications of moving the living room wall to make the hallway bigger, and the feasibility of adding an additional wc near where your workspace for visitors.

Accessing the downstairs loo via the utility is quite common so then you only need one door access from the bottom of the stairs. You could put the utility by the current garage door and as slim as 1.6m then use the rest of the garage for kitchen diner. Alternatively, use the light and access from the front of the garage for your new study and put the utility and toilet in the centre of your garage with one or two doors accessed from the extended dining area. Does that make sense?! If you want to have a chat over the phone and bounce some ideas around, feel free to get in touch. I can help with visualisations too if you need it. I offer 10 hours for £250 which gives people a really solid plan to work with and the confidence when sourcing their new kitchen from a supplier of their choice.

Do you want to be able to access the utility from the hall and / or the kitchen? Could you consider a wall halfway into the bedroom 3 space and use that as the utility? Would need a good extractor fan - and maybe some clerestory internal windows if you want natural light. Then you could have a door either side of that new wall - from hall-to-kitchen and kitchen-to-utility. And if needed a hall-to-utility door. I’d consider making the door from kitchen to utility - and maybe even the hall to utility - hidden for fun and also to avoid a “loads of doors” look. Could hide them in a run of cabinets for example.

Given the orientation of your plot, I'd suggest the proposed footprint is wrong. If you lose the single storey part and instead extend beyond your double storey extension with a single storey you create a southerly aspect. Single storey further than 4m is unlikely to worry planning - my 7m passed without comment. It's two storey bits where 4m matters. If you extend like that, how about kitchen where your architect put dining, and add a utility beside where the loo is shown - juggle it about a bit if you can to use the existing doorway and either access the loo via the utility or have a small inner hall with access to both.