I would not open conservatory but put a slider or more windows to it. I would for sure open between dining and living and I would add doors between lounge and dining. This is a typical UK I am guessing layout. Is there no powder on this floor? That would be a concern for me

There’s a 2 piece powder behind the stairs.

Once you remove those walls you have a lot of area to work with. I feel talking to a good design/architectural/contracting firm will be able to tell you what is and not possible when removing the walls. I feel an island is surely possible depending on where the kitchen is. For instance if the kitchen was along the store/utility room wall I can easily see an island. To make suggestions at this point is futile till you know what can and cannot be removed. This will be a full level renovation with everything being affected..

I do not know about the conservatory but in NA often these are not to code for living space sort od like a porch. You will need an architect for sure since removing walls is not a simple sledge hammer . I for sure would want the wall between the kitchen and DR removed if possible but I would leave the conservatory as is and do some nice doors there that can open wider . Those spaces can be hot sometimes and you might not want that heat in the house .The kitchen space is narrow so Island will take a real complete overhaul of theat space to even begin to plan an island. Are you planning to eliminate what I assum is the FR next to the kitchen area?

Have you had time to think about what we have asked? You will need to know what walls can come out so a strctural engineer is a must if all those walls Lorraine shows are coming out . We need some reply from you or tell us you do not need more help