Unable to attend a interview

I had a interview for a position and it was on the 10th May 2012 at 1.30pm . I spoke to my employers who run a taxi / coach company in Worcester where I live who said it was ok for me to have the time off and they would cover my clients that I take home from a day centre.
Well the company who’s interview I was attending phoned up and changed the date to the 9th of May at the same time.
When I imformed my employers about the date change they said they were unable to cover my clients and that I would have to work that day. The job is only 16hrs per week and the new job I was having the interview for was 37.5hrs. £16,000 annum.
The taxi company are the type of employers who would fire you for not turning up for work which  I cannot afford to do.

What would you all do in my situation ?