My Desktop is fitted with an HDMI socket and is compatible with Blu Ray but my monitor is not because there is no HDMI port.

If I purchase a monitor with HDMI and connect the HDMI cable with the Desktop and the monitor will I be able to view Blu Ray?

If not can anyone please advise me about what is required?

What do you plan on doing for sound?

Actually (I could be wrong) if all connections including the cable are HDMI 1.4/1.4a spec. capable, audio should be included in the signal. That means your desktop and monitors HDMI connectors have to be 1.4/1.4a too. If your desktop is an older spec you would need to use DVI (if the monitor has it VGA if not) and separate audio cables (red right - white left). A 1.4 spec will work for audio but having a 1.4a capable cable would be wise, for the short future anyway.