If you are running short on room for the family and have the budget to do a decent size extension, why not investigate an Orangery, It’s easy enough to find out what orangeries cost
This style of conservatory is functional, elegant & can add significantly to the value & desirability of your home.
This design, the Orangery, is substantial in appearance, often a combination of pillars, atrium style glazed roofing and will need you to sit down & plan exactly what you want before you start. Having said that, there are many companies out there in the UK which offer full consultancy & design services which include dealing with all aspects of planning permission & building regulations where needed.
In terms of what you get for your money, if you want space with class & a good return on your investment, then building an orangery Conservatory could be the best solution.