Hi, I'd back up the last answer in the fact that you do need two witnesses who are not beneficiaries, and stress the point that you MUST all three be in the same room when you all sign, as if you aren't and one of the witnesses later casts doubt the will can be said to be invalid.
Due to the small cost of seeing a solicitor I'd recommend you see one. You're 100% correct in saying you don't have to but if a solicitor costs you �50 - �100 now isn't that better than your kids / wife / parents paying thousands in unnecessary inheritance tax or costs through the delays probate cause just after your death when they'll be stressed anyway?
I'd like to stress I'm not a solicitor or even legal at all but find one you trust and they're worth their weight in gold.