Is there anything that can be done to make the employer change from a zero hour contract to a minimum hour’s contract?

A zero hours employment contract is a very specific type of working arrangement whereby an employee is required to make himself/herself available for work for the employer a certain number of hours or as and when the employer requires him/her to do with no guarantee of work.

In answer to your question, there is no legal requirement on an employer to offer an employee a set minimum number of hours, so the only way to achieve the type of change of contract in your question is by negotiation with your employer. Implied in a zero hours working arrangement is that there is may be no guarantee of work or hours in a particular week or pay period.

However you should note that there is limited