Am I legally entitled to plants out of the garden when I move ?

Broadly speaking the answer is yes – as long as you have your buyer’s agreement. However, the very fact that you’re asking the question suggests that you have not!
In this sense, garden plants are treated in very much the same way as any other fixtures and fittings associated with a property. In the preliminary enquiries sent to you by your solicitor at the start of the conveyancing process, you will have been given the opportunity to state exactly what you plan to take with you, and what you intend to leave behind – whether they be garden plants or carpets and curtains. Your answers to those enquiries form the basis of the contract of sale, so you can’t just go changing your mind about them afterwards. In fact, strictly speaking you would be in breach of the contract if you did. Moreover - although it is admittedly a bit of a grey area from a legal standpoint - the fact that garden plants may not be specifically mentioned in the preliminary enquiries does not absolve you of your contractual responsibilities. In other words, the basic rule is this: if you don’t actually state that you are taking something with you when you go, then the presumption will be that you are leaving it behind. If you subsequently change your mind, then you need to inform your solicitor as soon as possible.
This may sound like a lot of unnecessary fuss over a few plants, and in practice it is unlikely to cause a problem if you do take one or two. Your buyers may not even notice they’re gone – although they certainly will if you happen to take the one prize shrub that they particularly fell in love with, or if you leave your previously immaculate garden looking like the surface of the moon.
However, quite apart from any possible legal repercussions, it is simple politeness to get your buyers’ agreement before you remove a plant. Even if you previously gave formal notice of your intentions, it’s probably a good idea to mention it again nearer to exchange – just to avoid any unfortunate misunderstandings.