He led the congregations at St Augustine's Church in Locking and St Mary's Church in Hutton.
Father Peter Stodart, parish priest of St Augustine's, said volunteers understood the council's concerns.
The building has been boarded-up since June, forcing officials from St Augustine's church to make alternative arrangements.
BBC: Empty building dismays Tunbridge Wells Soup Bowl charity
Councillor Sophie Williams, who represents the estate as part of her St Augustine's Ward, said: she was "disappointed".
St Augustine's hospital has confirmed that it is helping police with their inquiries.
He was the pastor of St Augustine Parish in Bridgeport, Connecticut, for nine years, before he resigned in June 2011, citing personal and health reasons.
They are Dover Christ Church Academy, St Augustine Academy, The Duke of York's Royal Military School, John Wallis Academy, The Knole Academy and Wilmington Enterprise College.
He was then sworn in as the Archbishop of Canterbury by the Dean of Canterbury, the Very Rev Robert Willis, on the marble chair of St Augustine.
He said St Augustine's Parade would remain open the other side of central area and the old town area, to the east of it, would be car-free.
Lee previously officiated at All Saints' Church, Hempstead, before moving to Somerset to lead the congregations at St Augustine's Church in Locking and St Mary's Church in Hutton.
The Soup Bowl, in Crescent Road, was set up by volunteers from St Augustine's Catholic Church 24 years ago and is supported by other churches in the town.
The soup kitchen, which was set up by volunteers from St Augustine's Catholic Church, was given notice to leave the premises in February after the council said it was no longer suitable.
BBC: Empty building dismays Tunbridge Wells Soup Bowl charity
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