In the Anglo-saxon times the Dragon was often described as a Wyrm or worm. It was poisonous, long and scaly and often associated with serpents. Here are some descriptors of Dragons from Beowulf the earliest UK text that describes a Dragon in detail:

they saw then through the water/ many of the race of serpents, strange sea-dragon /exploring the lake

the wickedly coiled wyrm

since the fierce warrior had quelled the great serpent, the keeper of a hoard

until the one day, when he with the serpent must struggle. Then he went, one of twelve, swollen with anger, the lord of the Geats, to behold the dragon

So there is a lot of Serpent imagery associated with the Wyrm which forms the prototype of the early Germanic style of Dragon. It should be noted that Abbott Aldhelm, an early Anglo-saxon Christian wrote that the Anglo-Saxon pagans used to worship Snakes:

and because where once the crude pillars of the same foul snake and the stag were worshipped with coarse stupidity in profane shrines

So it seems that the Serpent imagery was already a powerful symbol in Anglo Saxon Mythology pre-Christianity and the representation of Serpents in the bible would have painted them in a villainous light.

In Greek Mythology the term Dragon can be closely linked to Serpents as well such as Python and covered well in this source. this influenced Roman Mythology and also contributed to the spread of Dragons and the inclusion of Dragons in the Bible also helped to spread the image of evil scaled monsters to the Anglo-Saxons.

As time progressed the image of a Dragon progressed further from the original 'Wyrm' or serpent like imagery into a more standardised winged lizard monster that we are more familiar with today. The movement from Serpent to Lizard seems to have taken place over many years but I can't personally seem to point out where this change originated from. Perhaps another user can help out.

So to answer your question more concisely. The Dragon or Wyrm as depicted in Anglo-saxon myths was heavily associated with serpents. This could have been influenced by negative depictions of serpents in Christian texts most noticeably in Revelations:

“He seized the dragon, that ancient serpent, who is the devil, or Satan.

But it could have also been influenced by elements from Pagan mythology and worship. If Aldhelm is correct and the Saxons did worship snakes then that could have further influenced the design of the snakish Wyrm. There is also the figure of Jörmungandr, the great serpent of Norse mythology. Jörmungandr is a good example of a giant villainous reptile that acted as an antagonist and villain. The concept of Jörmungandr would have been very familiar to the people of the UK due to Norse migration and conquests. Since the Anglo Saxons pagans didn't leave any written record it is impossible to accurately assess if a Dragon like create existed before foreign influence but I would say that the idea of an giant evil serpent seems to be a rather common theme in many global beliefs.