Do I need to take up floorboards from above to install spotlights to replace existing single lamp?

Depends on how much do you want to spend on decoration? Easier and cleaner from above. I.

In my opinion it is easier to approach from the floor above and sometimes taking down the dry lining boards but is not very practicable. The other way is to take up the floor boards and hope that they are aligned in your favour so that wiring is easier, if not then doesn't really matter just a bit more labor to the job. First I would mark out ceiling in kitchen so that they are all symmetrically balanced, mark each point with a screwdriver that you can push up into a ceiling so that way when you take up the floor boards you will see the light from the kitchen and you know that the spotlights will be symmetrically balanced, there is a chance that you may hit a beam, if so adjust the measurement so that you don't. It's probably likely that extra holes will be made in ceiling to get it spot on but that's not really a big deal it can always be patched up. I do advise that you are competent enough to carry out work as electricity is not to be handled without correct training.

Always a much nicer job if done from above, it can be done from the underside of the ceiling but is very messy, lots of holes and damage to the ceiling which if not in perfect condition can be a problem. Normally you will have to get the complete ceiling re-plastered if done from the underside. If boards come up, then this expense is avoided. All spotlights must be fire rated and building regulation approved so avoid the cheap Chinese rubbish. See info below: http://www.esc.org.uk/public/guides-and-advice/leaflets/downlighter-safety/