Which tires should I buy for an old road bike? I am upgrading an old road bike, which has Reynolds 531 tubing. (just to date it for you!)
I know the wheel dimensions: 700 x 28c, and have found several sets of tires, but am unsure which to choose. The bike will be used as a road bike, if that helps?

http://www.halfords.com/webapp/wcs/stores/servlet/product_storeId_10001_catalogId_10151_productId_249652_langId_-1_categoryId_242553

http://www.halfords.com/webapp/wcs/stores/servlet/product_storeId_10001_catalogId_10151_productId_811429_langId_-1_categoryId_242553

Any help much appreciated!
It depends on how you intend to use the bike. If you're intending to race, you'll probably want something lightweight and very grippy. If you're commuting or touring you should tend towards the durable end of the tire spectrum

With a nice steel frame like that you'll get lots of comfort, so it seems to "fit" with putting wider, comfortable, durable tires on it.

A wider tire is more comfortable with the only disadvantage being that it is a bit heavier.

If the bike originally had 28mm tires, I would expect it to take 25-35mm with no problem, but check the rims for any other indication.

The two you've listed don't have a great reputation for durability, so it may be worth investing a little more for something that will last longer and save you the frustration of punctures.

Consider Continental Gatorskins or Schwalbe Marathons. Both are more expensive, but offer good puncture protection which, in the long run, shortens your journey time more than a few grams of weight saving.