To show that 'criminal damage' applied, you (or the CPS) would have to show that your neighbour either intended to poison your plants or that he acted 'recklessly'.
Further, you'd have to show that the plants weren't simply growing wild on your land (as is often the case with ivy), as such plants can't be subjected to 'criminal damage'.
Lastly, you'd have to show he didn't have a 'lawful excuse' for doing so, such as protecting his own property:
http://www.legislation.gov.uk/ukpga/1971/48
In practice, such matters are often better dealt with by civil courts than criminal ones.