Albanach – it’s a bit of a ‘how long is a piece of string’ question, like asking how much it’d be for an architect to design a house on the same plot. Also depends where in the country you are. That London’s probably a bit more pricey than mid Wales.
You’ll get the ‘design and build’ companies who will do the design for nothing (then include the cost in the construction), the ‘pretty drawing’ type of designers who’ll do a sketch then hand it over to someone to (try to) make sense of, the ‘full service’ designers who will do an initial sketch then follow up with detailed layout plans for contractors, planting plans etc, and finally the ‘chartered’ designers who will do the same sort of thing but have ‘MSGD’ after their name which means they’re accredited members of the Society of Garden Designers.
On .5 acre you’ll probably need a topographical survey at some point in the process which would be a few hundred quid. I used to charge a flat rate for getting to an agreed sketch plan, then an hourly rate after that for the setting out plans, tendering, site visits, planting plans etc. Others charge differently – some even charge to come out to meet you so you can decide if you want to employ them!
It’s been a few years since I was involved but for 0.5 acre I’d expect current design fees to range anywhere up to 3 or 4K+ for a full service, up to 1500ish(?) for the initial plan. Build costs for something that size will be another consideration – you’re looking at the cost of a new (quality) kitchen as a minimum. I’ve done large projects where we split the build into phases over a couple of years so clients didn’t have to cough it all up in one go.