Labour group leader on the council Councillor Chris Ball says he was furious to learn Bexley had forked out £7,000 to send the former councillor to the USA for two weeks to take part in a leadership programme run by BT.
Although the cost of the course was met by BT, Bexley Council agreed to pay Mr Clement's hotel bills and flights and provided him with a car to and from the airport.
Mr Clement, now a £124,000-a-year deputy mayor with Boris Johnson, spent a week in Boston in May last year and a week in California last October. Cllr Ball says he understands the cost was personally authorised by former council chief executive Nick Johnson.
He also says many of Mr Clement's colleagues did not know about the trip until recently.
He said: "So there was not much feedback and cascading of information. And now Mr Clement has a new job, all this expertise is lost to Bexley."
The Labour group is also furious about the bill for refurbishing Mr Clement's office in Bexley civic offices when he was council leader, even though the building will soon be demolished.
Labour says an official inquiry about the cost showed £2,437 was spent on new furniture, £366 on new carpeting and £495 redecorating, with staff costs of £250.
Cllr Ball said: "Why was his office refurbished, when elsewhere in the building taps are leaking and windows are falling apart and no work is allowed except on health and safety grounds?"
He says the spending does not square with Mr Clement's boast of "value for money" and the end of grants for needy borough residents.
Mr Clement said the refurbishment of his office was "a modest affair" and that the furniture would be reused in the new civic offices.
He said: "And if Labour was worried about my trips why did it not raise it while I was leader? It is only being raised now because of the Christchurch ward by-election."
Questions may also be asked about 54-year-old Mr Johnson, who was paid more than £200,000-a-year while at Bexley.
He retired on ill-health grounds in November last year and is believed to have received a full pension and a six-figure pay-off. But in February, he resumed work as interim chief executive of Hammersmith and Fulham Homes. Mr Johnson's salary is believed to be £125,000-a-year.