(1) You can purchase the land for use as a garden. Planning permission is not required. You may very well find in the event that the vendor incorporates a clause restricting its use to a garden.
(2) I purchased a garden lump slightly larger than yours a short while ago. I offered �100 and settled for �150 plus an indemnity for the vendors costs. You can do the transfer yourself - your Local Land Registry will guide you through the process - but the company may instruct solicitors so budget �250 for them plus �80 to the Registry. If you DIY one very important point - you MUST get the company to impress the company seal on the Land Registry forms - nothing else will do.