Upvote:2
The safest answer is "quite possibly not".
It certainly does not work with Vodafone in some cross border situations.
Michael suggested that Vodafone will unlock it for money or free, but unless his answer is based on specific Hungarian and UK examples it's not a safe one.
A year or so ago Vodafone Australia refused to unlock a phone owned by my wife and locked to the Vodafone NZ network, even though it was many years old and obviously out of any contractual requirement for locking.
So, safest idea would seem to be to contact Vodafone UK and ask.