Many thanks for all your replies!
Firstly, I thought there was only 1 battery needed because instead of looking in the owners manual, I looked in the 'Rover 600 Electrical Library 1996' on page 4.3 where it says : "....Dependent upon use, the CR2016 battery in the handset should last 3 years....To change the battery...."
So 1 battery I thought. But was wrong....
Anyway, I put 2 in one fob and made sure that the +ve was uppermost on both as per the instructions.
The other fob had no batteries in it at all.
Replaced the buttons in both fobs, so they should be errr just like new now ??
Of course, neither remote fob works.
I have unlocked the car using the key, and then tried locking it 4 times with the fob but nothing happens.
Same for the other fob.
Now, as I re-read these battery replacement instructions, it says (in the owners handbook this time!) "Fit the new batteries ensuring correct polarity, +ve side facing up...." and I don't think the old batteries in one of the fobs were +ve side up, I think they were -ve side up.....
So maybe I am misunderstanding which way is up.......??
I'll try swapping them round tomorrow at work and then see if that works. I found without remote locking it's a proper faff in the dark (ok so I have only used the car in the dark once)....
What did make me laugh is that for the Owners Manual, on page 7 it is telling you how to fix your car! (to replace the keyfob batteries).
I never though of looking right at the FRONT of the owners handbook, I looked at the BACK, under 'Maintenance' where of course I didn't find anything about replacing key fob batteries....