Hi,
It's quite difficult to make suggestions on how to extend your house without knowing more about your house, particularly the layout of course, but also the council you are in and whether or not you have any permitted development rights.
In terms of permitted development, you would normally be limited to a 3m extension, but there is time limited legislation that may allow you to go up to 6m. Even under planning most councils have a mental cut off at 3m, but your specific building type, site location and neighbouring buildings can lead to approval for longer extensions. Some councils are more communicative than others during a planning application, and in those cases it is often an idea to ask for more and amend drawings back if the planning officer takes issue.
With my recent projects I am finding that clients are finding it much more useful to have some more intimate spaces rather than massive open plan rooms... However, every family is different and its important to consider how you and your family use your house (and to what extent that is down to the current layout rather than how you would like to live!) Some families revolve around the kitchen, others around the living areas. Some are always together whilst others prefer to have more personal space...
I would always recommend against a "design and build" company, because you lose the competitive pricing element when it comes to builders. Also, they will often give you "cut and paste" design, or design extensions that simply make their life easy (rather than yours!). Many of them offer "free design", but you always pay for this in one way or another so don't be duped.
You could use an Architect, or an Architectural Designer or a Technician. The first will often be much more expensive for you but all three could offer you the same services.
PS: I'm an architectural designer covering London and Herts, feel free to get in touch if you want more focussed advice.