It is understood that Mrs Bottomley wants to see some of the money go to help students at drama and dance schools which are finding it increasingly difficult to obtain discretionary grants from local authorities.
Both the DNH and the Arts Council ridiculed a newspaper report which said Mrs Bottomley wanted to sack Lord Gowrie and believed the Arts Council lottery awards to institutions such as RADA and the Royal Opera House were elitist.
This line finds favour with Conservative Central Office as a populist vote-winner. But the differences between Mrs Bottomley and Lord Gowrie are more complex than this. The Independent has learned that Mrs Bottomley did not oppose either of these awards, though she has told the ROH management that they do not always represent themselves to best effect.
But her real wish is understood to be for Arts Council money, be it from the lottery distribution fund or other Arts Council funds, to help dance and drama students. Using lottery money in the arts to help young individuals is now one of her key priorities.
Yesterday Lord Gowrie responded that there were "indeed frustrations about the distribution of lottery money" but both he and Mrs Bottomley were "prisoners of the regulatory system that Parliament had devised..."
He added that they had both adhered to the principle that lottery funds be in addition to and not in substitution for current programmes. "This, in effect, rules out using lottery money for the regular funding of dance and drama students," he said.
He echoed the words of the National Heritage Select Committee that "National institutions should continue to receive substantial sums of lottery money and be a source of national pride rather than envy".
Civil servants have warned Mrs Bottomley of potential problems in using lottery money or Arts Council grants to help dance and drama students. Once local authorities knew there was an alternative source of funding they would be likely to end the few discretionary grants they give now. With this in mind Mrs Bottomley is likely to devise a formula of using lottery money or government grant to the Arts Council to provide "a slice" of the grant for the students, with local authorities giving the remainder.