During the British Iron Age, large tracts of land in Southern and Eastern Britain were used to produce crops and the Celts who lived there were skilled arable farmers.
Image © Nigel Cross Pytheas of Massalia visited the Southern coast of Britain around Kent and the Thames in about 322BC. Unfortunately there are no surviving copies of his journal 'Peritou Okeanou' (About the Ocean) but later classical writers have quoted his work and they provide us with the earliest written account of Britain:
Thule was also described as being:
Pytheas' Journey c.322BC
He saw plenty of corn in the fields in the south-east but also noted the gradual disappearance of various kinds of grain as one advanced towards the northStrabo also repeated what Pytheas reported from Thule which he said was bordering on the frozen zone (perhaps the Shetlands):
...and he noticed that the farmers gathered the sheaves into large granaries, in which the threashing was done. Threshing floors being useless on account of the rain and want of sun.
... destitute of the cultivated fruits, and almost deprived of the domestic animals; and the food of the inhabitants consisted of millet, herbs, fruits, and roots. When they had corn and honey they made drink of them. 
Image © Nigel Cross
Pytheas of Massalia visited the Southern coast of Britain around Kent and the Thames in about 322BC. Unfortunately there are no surviving copies of his journal 'Peritou Okeanou' (About the Ocean) but later classical writers have quoted his work and they provide us with the earliest written account of Britain:
Thule was also described as being:
Just as today farming practices were not uniform throughout Britain. In some areas small granaries were raised above the ground on four posts but underground pits were more commonly used to store the surpluses of grain. These underground pits were timber-lined and their excavation, at places like Danebury Iron Age Fort, has revealed that offerings to the gods were placed at the bottom of the pits before harvest and possibly after a good harvest. Religion and farming were closely linked in Iron Age Britain. The classical author, Diodorus Siculus, was probably quoting the earlier writer, Posidonius, when he stated:
In reaping their wheat they cut off the ears from the stalk, and house them in pits under ground; then they take and pluck out the grains of just enough of the oldest of them to last for the day, and after they have bruised the wheat make it into bread.Farming methods remained substantially unchanged amongst the British peasantry from the Iron Age to the seventeenth century.
Oats, rye and millet are thought to have been introduced to Britain during the Iron Age. Spelt wheat was introduced around 500BC which is the Middle Iron Age and together with Emmer wheat became the one of the most important crops of the Iron Age. However, the farmers of this period also continued to grow barley and the less productive Einkhorn wheat. The productivity of ancient crops is studied at Butser Iron Age Farm. At this experimental farm it has been shown that good crop yields were probably achieved by the Celtic farmers. Some of these varieties may also have been more nutricious.
An organised system of land mangagement can be traced in Britain throughout the Bronze and Iron Ages. The high level of organisation can be seen in the way that the fields and paddocks were laid out in a structured way and on a vast scale. Celtic Britain, which spanned much of these periods, was an organised agricultural community and the 'celtic fields' of the Iron Age saw the introduction of a pattern of regular rectilinear fields. The evidence for this is clear from aerial photographs of land which has remained undisturbed. Demand for land was great and even the slopes of hill sides were cultivated.
Celtic field system - Burderop Down, Wiltshire. (c) Crown Copyright. NMR
Celtic fields can be seen in the bottom left corner of this photograph. They appear to be quite small compared with the modern fields which surround them.
In the later Iron Age (about 100BC) woodland was cleared at an unprecedented rate and some heavier soils were drained and made into farming land. By the first century BC the advanced Belgic tribes of Southern Britain certainly had an improved ard (simple plough) which had an iron ploughshare to move the soil to one side. The Romans are usually credited with introducing the coulter to Britain but the earliest example of an iron coulter, recorded in northern Europe, was found at the Iron Age fort of Bigbury in Kent. In fact, Pliny noted that the Celtic plough was superior to the Roman type which replaced it. (Think this was Rhaetia not Britain)
The island of Britain is recorded by the ancient writers as being very populous and therefore it is not surprising that there is evidence of soil depletion dating to the Iron Age. However, according to the Roman reporter, Pliny the Elder, the British farmers invented the practice of manuring the soil with various kinds of mast, loam, and chalk. He described how chalk was dug out from 'pits several hundred feet in depth, narrow at the mouth, but widening towards the bottom. In 70 A.D. he wrote:
...the chalk is sought from a deep place, wells being frequently sunk to 100ft, narrowed at the mouth, the vein spreading out within as in mines. This is the kind most used in Britain. It lasts for 80 years and there is no instance of anyone who has put it on twice in his lifetime.' 
These chalk pits can be found in Kent and are called Deneholes.
Few vegetables were known in Britain prior to the Roman Invasion of the country. However, Celtic beans and fat hen were grown and a kind of primative parsnip was found in Britain at that time. Herbs would probably have been the main way to get your 'greens'.