Don’t assume that you can automatically use the paddock as garden. This would be a change of use that needs planning permission. Given the outline permission shows a house filling most of the plot (presumably on an illustrative drawing), it seems odd that the paddock wasn’t brought into the plot when the permission was granted. Look up the application papers on the council’s website or call in at the planning department and have a look at the application file, in particular the officer’s report to committee. It may contain information explaining why the paddock wasn’t included.
Most councils are quite wary about extending gardens into agricultural land, but much depends on the surroundings and whether the change of use would be seen as harmful. You could also have a chat with a planning officer to see how he or she reacts. If the response is negative, it’s worth bearing in mind that people have been known to gradually domesticate land adjoining their garden, perhaps with the addition of the odd tree or shrub, and over time to subtly merge it into their garden. Such changes actually become lawful after a period of 10 years, assuming no one complains and the council doesn’t take action. You can’t rely on this ‘backdoor’ approach, so if a larger garden is a must, it could make better sense to find a larger plot.