Flying from England

The cheapest ticket is by Air Plus from Gatwik via Madrid on Saturdays, starting from 441 GBP (all taxes included).
Also you can fly daily with Iberia via Madrid, 3 times a week with Air France.
Night flights can be used by Lufthansa/Thomas Cook via Frankfurt.

You have a variety of connections via USA, for example: LON-NYC-SDQ or LON-MIA-SDQ, but you should clear immigration control, customs etc etc, which is not so cool these days!

Most if not all scheduled flights would be to AILA (Santo Domingo Las Americas) airport anyway.

The best route in which way? Check and compare prices, they will vary. As well as the two options you mention there is also Air Europa via Madrid, Air France via Paris, as well as other US airlines via NY, Atlanta or Miami. I've heard Martinair via Amsterdam offers good deals. I may have missed out some options.

Apart from Airplus and Iberia via Madrid, and Air France via Paris to Santo Domingo, Martinair and Arkefly via Amsterdam and Jetairfly via Brussels to Puerto Plata or Punta Cana are also possibilities. Which is the most convenient depends a lot on from where in the UK you're flying and on connections. I'm not sure how much Gatwick to Madrid flights are exactly, but my guess is Jetairfly via Brussels is the cheapest.
Chiri, Martinair doesn't have particularly cheap deals anymore, Arkefly and Jetairfly are a lot cheaper, so is Airplus, and most of the time even Iberia and Air France are cheaper.

My information is not that up to date. I need to find out about good deals to the UK for this summer, so I'll be watching closely.