Horse Tail/Mares Tail (Equisetum Arvense

Mainly found in the heavier damp soils.  During the winter it's not very evident, but has distictive shoots and foliage during the growing season.  It has a very deep rhizome (root) which you will be unable to dig out and it thrives on weed killer!  Several applications of weed killer on bruised foliage might work.  The rhizome system is extensive both horizontally and vertically and may reach over 1.5m deep.

Convolvulus/Bindweed (Convolulus spp.)

Several species, but it is identifiable in winter by it's underground white fleshy stems, these break off easily and each bit will form a new plant.  During the growing season the stems trail and climb and are very vigorous. In the summer it will have attractive white/pink flowers.  You can carefully dig out the roots and repeat dig and repeat dig.... or try Glyphosate weed killer. Roots may reach 1.2 cm deep after 1 year and 4 m after 2.5 years. 

Couch or Twitch grass (Elymus Repens)

A very common grass, but spreads rapidly by rhizomes or underground stems.  Digging out is possible, but it's easy to leave behind broken roots which will create new plants.  You can also try Glyphosate weed killer. 

Dandelion (Taraxacum Officinal)

Distinctive toothed leaves all the year round, the well known bright yellow flowers are followed by the downey seed head.  They have a fleshy tap root which will regenerate if left in the soil. The good news is, the flowers can make wine and the young leaves can be used in salads.  Be careful though as we have far too many, so there is no need to grow any purposely.  Seeds can spread up to 500m from the parent plant. 

Dock (Rumex spp.)

Distinctive leaves all year round, this plant has a very long tap root that will regenerate.  Grows up to 100cm tall and can produce a lot of seeds.  A large mature broad leaf dock can produce up to 60,000 ripe seeds per year! 

Oxalis (Oxalis Debilis)

You might wonder why such a pretty plant is a problem.  This originally started as an attractive ornamental, but is a curse on the drier soils.  It doesn't really appear until June when the clover like leaves will start to pop up everywhere, followed by these attractive pink flowers.  You probably dug the allotment in the winter or spring, totally unaware of the tiny bulbils hidden in the soil which your digging has broken up and spread even further around the garden.

Thistles

A biennial which spreads by seed in the Autum and can lay dormant in the soil for up to 3 years.  A persistent pest on most allotment sites, they seem to grow overnight.

Hairy Bittercress (Cardamine Hirstua)

This seems to be an insignificant weed as it is only 15cm high and pulls up very easily.  Once it has set seed it will be a difficult weed to eradicate because of its habbit of ejecting its seed up to 90cm when touched.  Then there will be several generations of this weed to deal with.  hoe or pull it up before it starts to flower.