What's the difference between a constitution and the memorandum and articles of association?
Not much - basically, older companies will have a memorandum and articles of association, and newer companies (basically those registered since 1 July 1998) will have a constitution.
The memorandum and articles of association of a company mostly contained what is now contained in a constitution, although there are fewer restrictions on what must be contained in a constitution (for example, a constitution does not need to set out the objects of the company, and does not need to provide a limit on the number of shares the company can issue (or "authorised capital")).
Both sets of documents basically provide for the terms of the relationship between the directors, the members (shareholders), and the company.
If your memorandum and articles of association or company constitution is old or has been lost, you can order an adopt a new constitution online.