This Act of Parliament exists to create a code for managing ragwort. It amends the Weeds Act 1959 . There is a great deal of misinformation on the internet about this Act. The practical implications for an individual are of little consequence, unless they are prosecuted for failing conform to a ministerial order made under that act. It DOES NOT place any legal obligation on anyone to control ragwort.
As can be seen from the rest of the Weeds Act 1959 there is no obligation for a landowner to do anything unless ordered to do so first. See Ragwort law for an analysis. The full text of the 2003 act is below.

Ragwort Control Act 2003

2003 Chapter 40

An Act to amend the Weeds Act 1959 in relation to ragwort; and for connected purposes.

[20th November 2003]

BE IT ENACTED by the Queen's most Excellent Majesty, by and with the advice and consent of the Lords Spiritual and Temporal, and Commons, in this present Parliament assembled, and by the authority of the same, as follows:-

Control of ragwort

After section 1 of the Weeds Act 1959 (c. 54) there is inserted-

"1A     Code of practice: ragwort

    (1) The Minister may make a code of practice for the purpose of providing guidance on how to prevent the spread of ragwort (senecio jacobaea L.).
      (2) Before making the code the Minister must consult such persons as he considers appropriate.
      (3) The Minister must lay a copy of the code before Parliament.
      (4) The Minister may revise the code; and subsections (2) and (3) apply to the revised code.
      (5) The code is to be admissible in evidence.
      (6) If the code appears to a court to be relevant to any question arising in proceedings it is to be taken into account in determining that question."

2    Wales

    (1) The reference to the Weeds Act 1959 in Schedule 1 to the National Assembly for Wales (Transfer of Functions) Order 1999 (S.I. 1999/672) is to be treated as referring to that Act as amended by this Act.

    (2) Subsection (1) does not affect the power to make further Orders varying or omitting that reference.

3    Short title, commencement and extent

    (1) This Act may be cited as the Ragwort Control Act 2003.
      (2) This Act comes into force at the end of the period of three months beginning with the day on which it is passed.
      (3) This Act extends to England and Wales only.

The Text of the act quoted here is © Crown Copyright 2003