People travelled for all sorts of reasons - migrant workers travelled back & forth for seasonal work, many less well off people moved to England permanently to avail of the employment opportunities of the Industrial Revolution. Gentry travelled back and forth all the time - e.g. to parliament etc.
There were many business connections, particularly in the cities, that could have lead to people moving temporarily, or even permanently to Ireland and vice versa. For example my own gt-grandfather was sent over to Dublin from Leeds to manage a branch of his employers mantle shops.
Shane