How to create a Matrix with available options.

Is it possible to create a form like the attachment where I prefill the times but the clients complete their name and contact number?

Yes, this is possible in JotForm. You can create the form by using the Input Table field. 

Just set up the input table field as TextBox.

Do let us know if you need further assistance.

Thank you that's perfect but what I need is when a name and a contact number is entered and submitted that the entry stays on the form so the next user cannot book the same time.  Is that possible?

Then you can use the MultiSelect Grid widget: https://widgets.jotform.com/widget/multiselect_grid, which will disable the options that have been already taken.

If you do not know how to add a widget to your form, please check this guide: https://www.jotform.com/help/252-How-to-Add-a-Widget-to-your-Form 

Thank you for your help but I don't think this is quite what I want.  I need to be able to type in the input boxes with a name and a contact number and for that information to be retained on the form.  As far as i can see this widget only allows the cell to be marked as selected.

I see what you mean, unfortunately, we do not have such a widget, otherwise, the next user could edit the already entered data from previous users.

Another option could be still using the Input Table field suggested by my colleague Chriistian, and creating a form report, such as HTML Table report: https://www.jotform.com/help/209-How-to-Create-an-HTML-Table-Listing-Report 

And embed it in your form through the Iframe widget: https://widgets.jotform.com/widget/iframe_embed 

If you do not know how to add a widget to your form, please check this guide: https://www.jotform.com/help/252-How-to-Add-a-Widget-to-your-Form 

The idea of an HTML table looks good but the table runs horizontally.  Is it possible to get the table to run vertically in the same design as the form itself which would be a lot easier to read.

You can see what I mean here http://boost.apps-1and1.net/booking-form

Your help is really appreciated.

Unfortunately, it is not possible to get the HTML table listing report to run vertically or edit/customize the table. It only allows you to choose what columns you want to include in the report and other configuration shown in the image below:

If you have other questions or need further assistance, please let us know.