Is there a reason for a second bedroom? I ask as given your budget and the current increasing costs of materials might put a full extension out of budget. Given that,  I also note that your current combined kitchen lounge area is larger than the bedroom, so it may be more within budget to think about the layout of these 2 rooms. I see that the current bedroom has an attractive outside aspect. If the kitchen is reconfigured you might be able to achieve this from this room with double doors located next to the gate. If it is possible to knock through between kitchen and lounge you could achieve an open plan or almost open plan in this area with the outside aspect. Some food for thought.........

If the second bed doesn't need to be so big, swap the bathroom with the box room. You'd need to lose the utility but would keep a nice big kitchen. If the budget allows, you could widen that room to line up with the living room wall. That'd mean a new kitchen which may be a stretch too far but the symmetry might be pleasing!

I'm stumped. Can't see how to do it well. So offering an alternative, though you probably already have this as a back up plan. How about dividing a room with furniture and curtains? Ikea do a sound absorbing curtain (mixed reviews) and googling "bunk bed room divider" finds some interesting images, also shows there are lots of people trying to give children their own space in a shared bedroom.

Just a quick question? Would you prefer the bedrooms together if possible? Were you thinking of an extension out towards the conservatory i.e. side return? I would do some room swapping and try and keep the bedrooms together and increase the size of the kitchen as it's very snug compared to the reception dining room space. The storage on the left is good to have but not at the expense of the room sizes and the corridor. There are so many possibilities but obviously all budget dependent. My instinct says you need a bigger kitchen directly connected to the dining/reception room and anotherr bedroom. I think a side extension although expensive as load bearing walls would give you more options. Removing chimneys is also very expensive.