Is it a semi or detached? Budget?
You could go all out with a rear and possibly wrap around extension depending on space to the side and garden size. But £££.
Cheapest is:
Knock through kitchen and living room, no room sizes on your plan but you may fit an island, if not a peninsula would work.
Use the existing reception room space which goes out onto the garden as the kids playroom.
Dining room as a living room with sofabed for visitors.
Convert the back section of the garage into a small office space. If a side window isn't an option you could borrow light with a glazed wall or door from the newly created kitchen diner into the new office space. We've done similar (we have a sun pipe and an external glazed door into our garden for light).
Got to weigh up the cost of the work and upheaval against buying a different or more expensive home. We've done a similar renovation 18 months ago including partial garage conversion, kitchen /diner knock through, new kitchen, some rewiring and fuse box, floors, some appliances, new doors, patio doors and windows, decorating for £65k. We could easily have spent another £15-20k if we'd gone for a higher spec kitchen, fancy utility fittings, LVT floors, solid wood doors, new furniture. You also need building regs, structural engineer report. We are in the North.