I'm also interested in the long afterlives of saints' cults, especially in England after the Reformation. Saints' cults survived in a number of different ways...
Firstly, they were perpetuated by expatriate English Catholics abroad, something that has been explored by Katy Gibbons and @onslies (with reference to St Thomas of Canterbury and St Thomas of Hereford). Often, relics played a key role in such perpetuation
However, some cults of English saints took on a life of their own outside England and no longer had much connection with England or English Catholics, such as the cult of St Edmund in early modern Toulouse
Secondly, saints' cults were preserved in England in clandestine ways by English Catholics - so, for example, the Catholic Tasburgh family of Bodney, Norfolk preserved a medieval manuscript about the miracles of St Etheldreda https://www.psupress.org/books/titles/978-0-271-02984-9.html
And lastly, fragments of saints' cults survived in folklore and popular memory - something I've written on with regard to St Edmund https://www.tandfonline.com/doi/abs/10.1080/0015587X.2015.1030909