Folks,
After going back and forth, the dealer offered 3 Year service (worth GBP 1,500) plan. Initially there was hard pushback from the dealer : 1) 14 days is applicable only on used car 2) Its not distance sale etc etc. After not getting anywhere with the dealer, I reached out to the corporate complaint department. They reached out to the dealer on my behalf. Not sure what helped, but the dealer offered 2 years service plan eventually. I asked for 4 year. Finally, we settled on 3 years. My main learnings from this adventure:
1) As pointed out by MrGreedy, Distance Sale is applicable only when its truly digital. i.e. one hasn't visited the store at all. So one has to be mindful of this pitfall.
2) Dealers are hard negotiators. So one has to be persistent with them.
3) Everything takes lot of time. So if your time is worth few KGs of gold then don't think about it.
4) Things go your way if you are on the right side of the rule (however convoluted it may be)