The hoary-looking leaves and dense, low-growing patches of this plant make it relatively easy to identify as a Grimmia, but otherwise it is a bit anonymous looking.
If you bear in mind that of the 29 species of Grimmia known in Britain and Ireland, only 4 consistently grow on limestone and other hard base-rich substrates, that makes identification easier, as G. dissimulata is one of those.
Of the other calcicoles, G. pulvinata and G. orbicularis are rarely found without capsules, leaving only G. dissimulata and G. tergestina, which don’t have them. G. dissimulata strongly resembles G. trichophylla, from which it was only distinguished in 2002. Some older records of G. trichophylla from limestone (it is a calcifuge) are likely to be G. dissimulata. G. tergestina is a rarer, much hoarier-looking moss that is mainly found on soft Jurassic limestone in the Cotswolds.