I need to re-paint the concrete window sills and lintels and a few other concrete bits on our house. I can scrape off the remains of the exisitng paint - much of which doesn't seem to have stuck to the concrete very well. It comes off in big flakes. Once I've done that, is thre any particular primer or surface treatment I should put on? The final coat will be gloss white.

Personally, I try to avoid using gloss on concrete wherever possible and try to use masonry paint because you can never be sure how well/long the gloss will adhere. (The same can be said for masonry paint in some circumstances though.)

However, when it comes to sills and the like, gloss is popular choice and if I come across problematic situations like you are describing, I will remove as much paint as possible before applying a coat of Zinsser BullsEye 1-2-3 and then applying a good quality exterior gloss. The BullsEye will adhere to nearly all surfaces and also works to combat the potential problems of alkali/salts within concrete which can be just one of numerous factors in paint systems failing.

Excellent! Many thnaks. I shall procure some.