A totally unexpected happy ending.
I continued my additional daily cold-start 2.5 mile Post Office trips for two months (as well as other short trips whenever possible) - and saw no real reduction in miles on the service indicator before the next service was officially due. I therefore thought "all was lost" and I would be, in effect, paying twice for the major service (once with the original service plan and then again for the actual service, when I had passed 38K without a service light).
But, knock-me-down-with-a-feather, just before Christmas with 37,850 miles on the clock the service light came on - with 1100 miles showing before the service was officially due. I could hardly believe it - but, again fortunately, a service slot was available. So, I booked in straight away and got the car serviced 'for free' under the original service plan, with about 50 miles to spare!
Talk about a Christmas surprise.
What, of course, I don't know is whether had I not increased my short trips for 3K miles or so the service light would have come on with 1100 miles to go, or more like the 500 miles others have suggested.
For anyone in a similar position, however, I would suggest the increase in cold starts (at least one extra every day - preferably two or three) is worth trying.
Hope this helps someone.