Upvote:1
The "can" and "plan" parts are conditions for the issuing of the visa. You are not violating the terms of the visa if you change your plans, only if you become unable to support yourself. If you can show sufficient funds to support your tourism, you should be allowed to enter. UK Immigration are quite used to Kiwis who had a British grandparent showing up and working short term jobs interleaved with long European holidays.
If you are still concerned, you can document the "can" part with a letter from your current employer saying how long you worked for them. The "plan" part is harder to document, as evidenced by the fact that they did not ask you for documents to support your intention when you applied! If they make looking for work a condition of entry, which seems highly unlikely, then you can always promise to apply for jobs once they let you in.
Upvote:2
NZ passport holders can visit the UK for up to 6 months without a visa. This should cover your tourism needs. Immigration would want to be satisfied that you don't intend to work etc when you re enter. Edit: depending on your circumstances you may want to become a dual citizen, which is allowed by both UK and NZ.