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Some advice: if you are not a morning person, if it takes you a while to get going, to collect your thoughts, to syncopate with the day, then do not arrange an 08:00 GMT interview with Dame Vivien Duffield. By this time the jewel-eyed philanthropist is as feisty as a terrier in a field of rabbits.

As I found out when we met today on the National Theatre's rooftop terrace. It was a chilly but beautiful morning. A Monet-like mist, lit by a rising spring sun, made for an evocative scene as boats glided calmly up and down the Thames going about their daily business. Not that we chatted about that. No, we got straight down to business.

"What do you think of the budget" she asked.

"Err...well...I was..." I began.

"A good start don't you think?"

"Hmm...perhaps...I thought...do you think they've got any coffee around here?"

"Jeremy's [Hunt, the Culture Secretary] done well to wrestle those concessions from the Treasury"

"You think so...?"

She does. She is delighted with the tax breaks announced yesterday by George Osborne in his Budget, which she calls "a step in the right direction". And has visibly warmed to the culture secretary. The last time we met she wasn't that pleased with him. He'd made a big play about writing to all the country's philanthropists, but Dame Vivien - one of the most generous - had not heard from him. Communications appear to have improved since.

And having spoken to other philanthropists and the recipients of their generosity in the arts, there is a general feeling that Jeremy Hunt's initiative to encourage more philanthropic giving is starting to pay dividends. His simple and ultra cost-effective idea of making philanthropists feel more appreciated is proving effective. But, as the culture minister made clear when launching his campaign last year, philanthropy is no substitute for government core funding. Nor for that matter, are one-off lottery grants.

Theatres, museums and orchestras say they need core funding on either a three, four or five year contact, to enable them to plan and run their businesses. Any additional money provided by philanthropic gifts or a one-off lottery grant is extremely helpful, but doesn't compare. It is the difference between an employee earning a wage and then receiving the occasional bonus, you can plan your life around one, but not the other.

So while arts leaders acknowledge the efforts the government has made to increase philanthropy and the positive changes they have made to the lottery, there is still a great deal of concern about the cut to their core subsidy which ranges from a minimum of 15%, up to nearly 30%. This, they say, is significant and will affect them materially. Their programmes will have to be reduced, with many citing their educational outreach work being particularly susceptible.

Already Creative Partnerships - the nationwide programme to connect schools with the arts - has had its funding withdrawn, all £40m of it. That is a huge sum to remove from children's arts education, an area many consider to be the most crucial role played by the arts in Britain. And because education is not seen as "front line", it remains very vulnerable to further cuts. If you look at most fundraising proposals prepared by arts institutions, you will see that they are for - or at least contain an element of - education and outreach.

By most measures the subsidised arts sector in Britain has been successful over the last decade. But the one area that almost all arts companies have struggled with is in diversifying their audiences; the vast majority of their customers are white, middle class and tertiary educated. They want to change this, to reflect and serve their communities better, and recognise that education is the way to do it. As does Dame Vivien, but she can't do it all on her own.