Best time to make a pond repair?

The best time to do a repair is in the late autumn - as if there are newts using the pond then this year's tadpoles will be turning into little newts and leaving the water from mid August through September into early October. (It depends whereabouts in the country you live, the further south the earlier). Frog & toad tadpoles leave much earlier and there probably won't be many left now.
Some tadpoles may still not have left the water and some adult frogs may hang around in the pond all year. Therefore if you have some buckets or large containers you can save some water, plants and animals to re-introduce back into the pond after you have relined it.
Try not to fill it with tap water as in many parts of the country it has relatively high levels of nitrates that can encourage algae. If you can divert rainwater from the house gutters into the pond or into water butts from which you can fill the pond, so much the better.

Hi, newt tadpoles do not look like frog or toad tadpoles but by this time of the year will look like very small newts with feathery gills at the sides of their head. The tadpoles remaining are probably frog or toad - frog ones are generally chocolately brown and speckled whereas toad tadpoles say black until they metamorphose into toadlets. 

Just to add to Chris's comment re newtlets. I have some in my pond and they are very dainty creatures - easily overlooked. Not so hefty as a tadpole of frog or toad.