There are two species of Claytonia (formerly known as Montia) that are useful in Scotland. Pink purslane (C. sibirica) is a shade-tolerant, carpet-forming perennial with pretty pink or white flowers. Its leaves are used in salads, with two caveats: they are fairly small so it takes a while to pick them and, personally, I don’t like the flavour at all. They are worth trying though: if you do like the taste they are a very attractive, easy, low-maintenance plant for deep shade.
Miner’s lettuce (C. perfoliata, also known as winter purslane or spring beauty) shares pink purslane’s shade tolerance but otherwise is a quite different beast. It is an annual and has to reseed itself every year – once established it is likely to do this quite enthusiastically. It has a mild flavour and makes an excellent salad. The whole plant can be used, even when it is in the early stages of flowering, which makes picking quite easy. It is generally productive during winter and early spring, running to seed by late spring. It is usually grown as a greenhouse crop in Scotland but why is a bit of a mystery to me as it seems to thrive outside.