According to Google, St Mary's, now St Helen's is Church of England.
Swindon was an early and important centre for the railways, googling it will give you heaps of information.
But before you waste lots of time on Swindon, I would order the death cert for Edmund. If you want to be cautious about spending your money, you could look at the 1841 census for Swindon to see if you can find an Edmund Twist. If you have already found your man in Haydock in 1841, well, he can't be in Swindon at the same time, can he! Also look at IGI to see if there are any TWIST families in Swindon at this time. If you do get the death cert and it is your Edmund, you will have a date of death and burial will be a week later at most. His widow may have put a notice in her local newspaper or there may be an article, again a week or two after the death which may give you extra details (where buried etc). Finally, with an approx burial date, someone in Wiltshire may do some lookups for you.