Yes, providing she can get it unlocked in the UK, she can use it in those countries.
There are different mobile phone systems in the world, but basically a decent UK phone will work internationally except in North and South America, which use a different system. Whether your phone works in America depends on the phone.
It is even possible to buy a foreign SIM card on the Internet before she goes. The advantage is that she could tell everyone her Sri Lankan number and her New Zealand number before departure. The disadvantage is that it will obviously cost more than buying it locally. Alternatively she could text people her new number on arrival.
Don't forget that in the UK you can get a locked pay-as-you-go phone for �9.95 if you buy �10 credit, so maybe you can do the same kind of thing in Sri Lanka and New Zealand.
In Sri Lanka, coverage will be limited. Have a look at this map:
http://www.telestial.com/view_product.php?PROD UCT_ID=LSIM-LK01
If she's going to be in one place, see if it's covered. If she's moving around, bear in mind that there will be long periods when she's uncontactable.
A website where you can buy foreign Sim cards is:
http://www.telestial.com/sim_cards.php
This one is in the US, but they do ship internationally. You can probably find one in the UK though.
Lastly, she'll need a power adapter. It'll be easy to buy one in a Sri Lankan city.