The designation of specific services and activities is set out in the Health Act 1947 (Section 31A - Temporary Restrictions) (Covid-19) (No. 8) Regulations 2020 which were made by the Minister for Health on 21 October 2020. The Regulations set out the grounds on which a person may leave his or her place of residence and it is a for individuals to determine whether particular activities qualify as essential.
While local authorities are entirely independent corporate entities having full responsibility under law for the performance of their functions including the reserving of land for use and cultivation as allotments, and for regulating, promoting, facilitating or controlling the provision of land for that use and I have no function with regard to the operation of allotments it would appear that activity in this area would qualify under the "Agriculture, horticulture, forestry, fishing, animal welfare and related services" provision of Part 2 of the Regulations.
It should also be noted that there is no limit per se on travel distances needed to access essential services or engage in an essential activity; the 5km distance restriction from a household applies to travel for the purposes of exercise.