Got a letter from Ford telling me my "base warranty is expiring".

Bit stingy, I (wrongly) thought it was 5 years not 3.

Begs the question, what exactly is the "base warranty"? Is there a "non-base" warranty that still exists?

In the smallest print know to mankind, I was offered "Ford Protect Gold Extended Mechanical Breakdown Insurance"  (protect, gold AND extended....they are really selling this).

What is this? Is it merely the AA or RAC towing you to a Ford dealer for repair?

edit: just looked into this. It's basically £300 a year (bound to go up as the car ages) and Ford will repair what looks like an enormous list of mechanical and electrical issues. Of course, the devil is in the details, and I can imagine the situation where - conveniently for Ford - the exact mechanical problem is somehow not covered.

Anybody have experience of this insurance, and have used it?

I'd start from the tiniest print to see if it is worthwhile for you.
CAR (Cash Always Required)?
If you have had no problems i.e. have solved any "child mortality"  issues, you should be into the long section of the bathtub curve where only normal maintenance is required?
These warranties, as you say have multiple exclusions needing very careful reading.
The biggest one will be wear and tear so no new brake pads, discs, tyres, ??? etc.
The other way is to put aside an increasing amount starting at the £300/year (you'll get the interest)  to cover anything above normal maintenance and "self insure" - always need to be putting cash aside for cars anyway so, if you choose, better to keep it yourself rather than give it to Ford depending on your views (they are not your mates)
You may win or not, there's always a risk.
Even if a large repair, you keep the car and write it off over multiple years still cheaper than cost to change?

For context, we have owned 2011 vehicle since it was about 6 months old and, apart from servicing it has only had a wheel bearing (likely due to going over an unavoidable brick on M1), rear drop links, 3 batteries (there's another warranty exclusion list, it only covers manufacturing faults), a couple of welding jobs on the exhaust a fuel filter housing and a vaporiser plug plus inevitable bulbs. All expected and, so far reasonable.
I think at 15 years we are starting to get into the "wear out" phase of increasing work but that, again, is to be expected.
 

yeah, I am extremely skeptical of extended warranty deals. By definition, the average punter loses.

My cousin is a vat registered mechanic, owns his own small business, so I can always get "mate's" rates on most things (so long as I don't take the p1$s...). 

Unless people have good advice to the contrary, I think I'll stick with regular servicing and maintenance and get it fixed if and when necessary.