When you say "sun room" do you mean a conservatory or a proper extension built as a sun room with full building regs?
Whatever you do, don't go down the conservatory route. I don't know anyone that is happy with them. Expensive, too sunny, too hot then too cold
We had a full blown extension with loads of Velux windows and sliders. We have underfloor heating and at is a totally delight. Usable 12 months of the year whereas our neighbours just can't use their conservatory except for storage?
We added on 40 metre square and reconfigured all of the old kitchen to make a utility with new kitchen, living area and dining area. It is huge
Total cost was circa £80k but includes the kitchen with quartz and a utility kitchen. Built to a high standard in stone with replacement external doors and 60m of laminate.
If you do extend, my advice is to avoid lantern windows in a flat roof as apart from,the flat roof, it is difficult to manage the sun coming through. Also, we found sliders better as better view and less to go wrong but if you don't have a big opening you might be forced to use them. We had 5 metres so worked well
Good luck