Bob,
The letter of the law (for a car of your age) is that the windscreen must allow at least 75% light through, and the front windows at least 70%.
Did the plod measure the light able to pass through window in three seperate places using a device in a black box (known as a tint-man?)
If so - what were your readings?
If the light allowed through was significantly less than the 70%, then you could be issued with an endorsable fixed penalty notice for using the vehicle in a dangerous condition.
Where the light is below the limit, but not by a great deal, it can also be dealt with by way of a non-endorsable £30 FPN.
I think the officer probably got it wrong re. the 3 points per window. If the tints are very dark, the offence is a singular one, of "using the vehicle in a dangerous condition", so would only attract one penalty of £60 and 3 points at worst.
If there were further offences, they'd have to report you for summons.
They also have the power to prohibit the vehicle if the tints are dangerous, but again this is highly unlikely unless the levels are very very low.
Either way, it sounds like he used some common sense, and made a good judgement call with the words of advice 
Thanks for that James. 
He didn't measure the light but said he could arrange for it to be tested in which case if it failed he would definitely have to nick me.
Not sure why he said 'have' to nick you.
Obviously I wasn't there, but it sounds like he needs to think about exercising a little discretion.
Ultimately, what is his aim by stopping you for tints? The answer to that is road safety.
If by offering you advice (peeling them off), which he thinks you are going to take, this objective becomes achieved, the requirement for him to 'nick' you isn't there.
Either way, not to worry, you avoided a ticket
