Wouldn't you know it, I just found the lyrics online after my first search turned up nothing. So here they are, from http://www.billprince.co.uk/nocauseforalarm.php

No Cause For Alarm
I do unfortunately (for me!) have a tendency to write songs with a "sing-by" date on them! "No Cause For Alarm" is an example of that - some of the things mentioned in the song are no longer relevant. In an effort to redress this I wrote some new verses in 2004, but I've only sung them once - somehow it didn't feel right. Perhaps it’s just too ingrained in my head in the original form.

This song was recorded by Red Shift on their album, Back In The Red; when John Adams played me a snippet of their arrangement in a North London club, I didn’t recognise it at first.

No Cause For Alarm       © Bill Prince 1984/2004
A-tests on Christmas Island       No cause for alarm
Cover your face with your hands       No-one will come to harm
Follow your orders, do as you're told
The situation is under control and there's
No cause, no cause for alarm

Power station at Windscale       No cause for alarm
Safety measures that can't fail       No-one will come to harm
We've paid compensation to three or four men
But rest assured it can't happen again and there's
No cause, no cause for alarm

Research lab at Teddington       No cause for alarm
Working with Uranium       No-one will come to harm
Though there's been a slight leak for about twenty years
The experts confirm that there's nothing to fear and there's
No cause, no cause for alarm

Cruise missiles at Greenham       No cause for alarm
American soldiers to guard the       No-one will come to harm
They're just a deterrent, what's all the fuss?
They won't push the button without asking us and there's
No cause, no cause for alarm

Nuclear waste dump at Elstow       No cause for alarm
It has to go somewhere, we all know       No-one will come to harm
We'll bury the waste deep under the clay
In two hundred years or so it will decay and there's
No cause, no cause for alarm

Government at Westminster       No cause for alarm
There really is nothing sinister       No-one will come to harm
Though we keep a few secrets it must be understood
We can't tell you everything for your own good but there's
No cause, no cause for alarm
No cause for alarm
No cause for alarm

New (replacement) verse 2
Power station at Windscale No Cause for Alarm
Safety measures that can't fail       No-one will come to harm
There's fire in the chimney, worst incident yet
But we'll just change the name and they'll quickly forget, so there's
No Cause, No Cause for Alarm

2 New verses
Weapons of Mass Destruction       No Cause for Alarm
We know that Saddam must have some       No-one will come to harm
He's hidden them well, on that you can bet
So it isn't surprising we've not found them yet, but there's
No Cause, No Cause for Alarm

Back up at Windscale again       No Cause for Alarm ( I refuse to call it Sellafield)
We're missing some plutonium       No-one will come to harm
It's just thirty kilos, a trivial amount
And we've not really lost it, it's just we can't count, but there's
No Cause, No Cause for Alarm