It is possible to sow some early seeds in January. Tempting though this is, there can be problems. Early in the year the young plants cannot go outside, potentially for several months, which means you need plenty of space to grow the seedlings under glass to protect them. Everything you sow now/or buy from the garden centre as a plug plant will have to be grown under glass until frost is over. If space is short, it's best to wait until later in the year.
That said, January is a good time to sow Chilli seeds because they need a long growing season in order to fruit well. Chilli seeds need both heat and light to germinate and here is more information about growing Chillies from seed.
It is also still cold, and to germinate seeds need warmth, such as a heated propagator and then transferred under glass. Once established, some seedlings should be OK in the greenhouse, (but not all,) unless it is very cold, when cover with a fleece. Sowing early can be a bit hit and miss and only sow hardy or half hardy seeds with protection.
A heated propagator mat is good if you want to get seedlings going early. The average conservatory/greenhouse is too cold to germinate seeds, and this heated aluminium mat (illustrated left the propagator trays stand on it,) is ideal to start off germination. More Advice on how to germinate from seed and a short video looking at growing veg from seed.
One of the main problems growing seedlings at this time of year is not just the cold, but also low light levels. This can cause seedlings to be spindly and leggy. Often light is from one side only, and the seedlings become leggy growing towards the single source of light.