Until 1821, the only church/burial place was St Cuthberts in Churchtown for any North Meols/Birkdale folk... and even after the new churches arrived, marriages and burials still often took place there, being the traditional place of their background. However, as Michael was born in Formby, he would have no emotional links to St Cuthbert's (and Cantwell wasn't a local family, so it's likely his wife wouldn't have a family tradition to follow either). That being the case, I would guess that Christ Church would be the most likely place of his burial, which opened in 1821 and was the primary location of baptisms, marriages and burials for those living closer to the new Southport than to Churchtown.
The burial ground at Christ Church no longer exists, and the few gravestones still there have been used as paving stones for the path.
There are one or 2 other places he might have been buried, such as Eastbank Lane Congregational, but this closed in 1966.
The main cemetery in Southport was not built until 1866, and would probably have been the family's choice if he'd lived until then, as it was built on Snuttering Lane (which became Cemetery Rd). If his wife survived until after 1866 and remained in the vicinity, I would imagine she was buried there, which might be your best chance of finding further information on the family from grave inscriptions.
Impy