I would say the bare minimum you'd need to go for really is around 1.5m in either direction. That will make your Kitchen run of cabinets 2.8m long. I don't know what the layout of the kitchen is, but you can save room by having a washing machine under the drainer of the sink etc. If you can lose basically a 1200mm double base unit plus another 300mm then it may be do'able. All depends on what you've got where really.

I'd do exactly as Jonathan has done on the ground floor. The first floor can be re-configred in a miriad of ways depending on whom you wish to afford it to ie;- The boys and the Nanny, I'd still try for 3 bed, and En-Suite and a main bathroom. I think that whomever is using it, then you'll need an En-Suite either for yourselves or your Nanny. So something like this may work well. The loft is a whole different kettle of fish. 2 metres is okay - you can stand up in there. I'd certainly get rid of the pointless utility room and turn it over to storage as you have 3 boys, you're bound to need quite a bit. It's possible that you could re-arrange the entrance slightly and donate the long thin area over to a playroom, giving them more space to play indoors.

Your house looks a similar dimension to my house which I just sold. I kept the wall dividing the receptions rooms but took the wall down between the kitchen and back reception room. My kitchen was in a little out rig (original not extension) but i think you could do something similar? https://www.rightmove.co.uk/house-prices/detailMatching.html?prop=50634231&sale=5936314&country=england

I think 1200 is a good clearance- I have 1000 which is fine but they reckon that 1200 is right if you have two people in the space. If you had a smaller island I think the island would look too small so I wouldn’t make the walkways bigger. In addition you currently have a foot hole for the stools that is 2200mm- in my opinion this is more comfortable for 3 stools than four so you certainly don’t want to go smaller. In fact you may want to swap the 300mm units and replace them with end panels. I hope you don’t mind other observations too. To continue the symmetry I think I would centre the range to the wall and island. Perhaps 900mm drawer units each side of the range would fill the space and personally I would rather have drawers there than behind you when cooking. I think I would also swap the extractor hood for something more decorative since it is the only thing you see when sat at the island. For me I also feel that the American Style fridge has had its day in high end projects and I would rather see two integrated appliances. You could have a side by side larder fridge and larder freezer that would have more chiller space than an American Style fridge or you could have 70/30 fridges side by side. You can get a 900(ish) wide integrated fridge freezer too but this is often a more expensive option. For visual interest interest you could fit this wall with a breakfront. Personally I think the island is one place you don’t need symmetry. Personally I would put the prep sink at one end so the prep area is uninterrupted. I would also include a large pull out bin cupboard so you can easily dispose of recycling and food waste. The island also seems like a great place to integrate a microwave rather than having it cluttering a worktop. Lastly I think I would probably add either some wall cabinets or paint the sink wall in the cabinet colour to balance the tall units at the other side of the room.