Hi
He died on 23rd September 1707 according to the entry in Wikipedia
Entry from St George the Martyr Southwark's burial register
29th September 1707 St George the Martyr Southawrk
John Tutchin The Observator in St Georges Street in the Mynt buryed at Christ Church in Surrey
Christ Church Churchyard was at Blackfriars Bridge Road though you might expect a burial entry in that church's register if he was buried at Christ Church (though non-conformists are not always mentioned in church registers as there would be no service and burial would not be in consecrated ground). There is nothing in the register. It could not at the time have been called Blackfriars Bridge Road since the first bridge wasn't built until 1769. The churchyard was closed in 1856 and opened as a public garden in 1900.
He was apparently 43 (his elegy stated)
In 1707 the Queen's bench prison was at Angel Place, off Borough High Street, Southwark. I think John Tutchin probably lived in the Liberty of the Mint. I'd be less sure the Queen's Bench prison was actually in the Liberty but it was certainly adjacent to it.
http://en.wikipedia.org/wiki/Liberty_of_the_MintRegards
Valda