Vegetables can be grown indoors, but you must choose the correct conditions and vegetables. The main condition is light, which must be maximised for vegetable growth. If you have a conservatory, all the better, as this is small greenhouse attached to the house, but you can use window ledges. These should be south facing to maximise sunlight. They should also be free of draughts, as cold draughts can damage sensitive plants.
Containers need to be properly watered, as they dry out easily. But you should not overwater them, as this can drown the plants. The growing medium should be kept moist, but not soaking.
You also need to ensure that the medium contains enough nutrients. Soil in containers will soon run out of nutrients, so you need to add fertilser at a regular rate, every two or three weeks. But you must not over-fertilise, as doing so can damage or even kill the roots. Follow the manufacturer's instructions on the fertiliser packet. You must also ensure that the medium is suitable for the plants that you want to grow. Most plants grow happily at pH 6.5-7, but some plants need a higher or lowe pH. pH is the ratio of hydrogen ions in the soil and measures acidity. A low pH is a highly acid soil, and a high pH is high alkaline. You can measure the pH with a special measuring kit easily purchased from a garden centre. If you are growing annual plants that last for only a year, then the soil can be changed every year, but if you are growing herbs that you want to ensure for more than a year, you may need to repot them yearly. This means taking them out of a container and potting in another, possibly larger one.
Do not allow plants to sit in still air. They need a flow of air around them. This is to provide the carbon dioxide that they need. It is also to prevent a build up of humiditiy that can cause fungal diseases to set in.
Select your plants carefully. I have seen a banana plant growing in a corner of a room, but no bananas came from it. The problem was that this plant has a high light demand, and a corner could not therefore provide enough light. Tomatoes and peppers are excellent for indoor growing. They grow well on south facing window ledges, even in cold climates. You might also be able to produce aubergines in similar conditions, as these are plants that grow better in protected conditions in the British climate.
Herbs make great indoor plants, as they are small and can easily grow on window ledges. Basil, thyme and sage grow well in containers. They can grow on the kitchen window ledge, if it receives enough light.
Mushrooms can also be part of your indoor garden. Contrary to common belief they do not require darkness, but they do not like over-much light. Unlike plants they are air breathers, so they need a flow of air around them, though ideally not a cold breeze. Mushroom kits cna be purchased from some garden centres and a number of suppliers on the internet. A cellar or the space under the stairs can be an ideal mushroom cultivation site.