I am new to this so please forgive me if I contravene group etiquette. I have all of four years experience of an allotment near Roundwood Park
As its now January, its too late to answer the above, but if the question had been asked in October, when the ground is still warm, I would say peas and broad beans (Aquadulce). The plants will grow until the frost comes and develop their roots to provide an early crop in May. They are completely hardy.
TOP TIPS for January
Don't dig the ground if it is frozen! Even if you can turn the soil, your activity will bury the frozen ground and it will take weeks or months to melt.
Get your muck/compost heap sorted! I think the minimum is to have two heaps so one is rotting while the other is being built up. So if you have not got one, now is a good time to prepare two compost bins. Please don't buy green plastic 'daleks' they slow down the decay process. Two square 3ft x 3ft bins 3 or 4 ft high is good for a medium-sized garden. Some people use pallets or other scrap timber. You can even buy them in kit form! If you already have a heap, now is a good time to dig it out, spread the soil-like material on frost-free ground and use the unrotten material to start a new heap. When you come to sow in the spring you can fork in the compost.