Do I have to declare unsold equities in my self-assessment?

pieroabcd

HI
at the beginning of the year my employer assigned me a set of stock equities (RSU) that are traded and held by a fund in the US.
They also made me sign an S431 form.
Of course the equities had an initial nominal value that has gone up and down ever since. 
I've never sold them.
My employer is ignoring every queston related to tax matters.

My doubt is this: if I don't sell the equities, do I have to declare them in my self assessment and pay tax on them?  If so, what's the equivalent value?

I imagine that I will have to pay tax only when I sell them (after all I haven't received any money yet), but since these is not the subject on which I can take risks I preferred to ask.
The S.431 complicates matters a lot for me because it's far from crystal clear. I can only understand that when taxed the value of the shares adds to my taxable income instead of paying the usual CGT, but there seems to be much more than that.

Thanks.