Have you considered a stackable washer and dryer OR a combo unit that does both? Am I correct in thinking that you are in the UK? I know that combo units are available there. Changing the location of your toilet will be expensive and will probably mean that you must retile your floor. I would leave the toilet where it is. Remove the utility sink and place the stacked units there. You might be able to squeeze in a larger vanity, but that would depend on the distance of the door swing of your unit/s. If you get a combo unit, you might be able to create a cabinet on top of it for folding. And perhaps hang some shelves or a wall cabinet above that for storage. How will you vent your washer and dryer? I don’t see a place for that.

European baths are often like that with washing right in there but there is really no need for 2 sinks, not much handwashing is done these days. I like Ptreckel's advice - a stackable set where that sink is and then a new vanity to fit once that is in - maybe with sink to the right side so you have a little bit of counter space.