You could do it by a codicil but a new will would probably be better (leaving less room for misinterpretation of your wishes).
I use to draft wills for a living. My advice would be to get hold of a copy of this book
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It's in almost every public library; it won't matter if it's an older edition. (While the law on intestacy has changed fairly recently, the basic stuff about writing a will remains valid).
Then draft your own will, following the advice in the book. If you're absolutely 100% sure that you've got it worded perfectly, type it out on plain paper and sign it in front of two witnesses (who shouldn't be beneficiaries under your will). It's an easy process and no great formality is involved. (My own will was witnessed, by a couple of people I happened to be working with that day, in a Tesco car park!).
However if you've got any doubts about your draft, then take it to a solicitor and say 'Tidy that up for me'. (Remember also that some charities provide a free will-writing service to those who'll leave them something).