Bizarrely, it seems that, as from 30 April 2016, it will be extraordinarily cheap to roam within the EU while using a Vodafone UK SIM. The new prices are given here, and are very much below the standard prices for using one's phone within the UK. Unless you will be using your phone very heavily, EuroTraveller for PAYG is unlikely to be to your advantage.
I don't understand why this should be, and can only think that the English translations of the new rules leave a lot to be desired! However, I am seriously considering getting a French SIM to use while in the UK.
There are a couple of snags - the first is minor, in that you must ensure before going from the UK to Europe that your account is enabled for roaming - see the notes here. The other is more significant, as to top up a Vodafone UK account from outside the UK would require either a UK-based credit card, or to have some UK top-up vouchers with you. However, you could ensure that your account is well topped up before you move on from the UK, and then get a local SIM when the money runs out!
While you are in the UK, calls back to NZ would be relatively inexpensive provided you opt into Vodafone International. But this wouldn't work outside the UK - for that, a local SIM might well be more effective.
