Everything you do, from where you have lived, to where you have worked (legally) is recorded.
There are many companies specialising in this data, example: http://freerecordsregistry.com/check-employmen t-history.htm
So the answer to your question is a very definate YES.
Don't be scared off by this as I doubt many bother. However, honesty is the best policy.
the P45 has your previous employers details on it, but I believe you can write to the tax office and request that the details are not given on the form.
What an employer may think if you withhold this information is up to the imagination.......