I've come to this thread late and I admit to having only skimmed through some of the previous answers. However it seems clear that we've at least established that the beneficiaries of your will can also be executors (and that it's witnesses who can't be beneficiaries).
However you seem to be assuming, JennyJoan, that you need a solicitor to make a will and that everything has to be done in their office. You certainly don't need to use a solicitor but (unless you're 100% confident about doing it yourself) it might be best to use one
as a final step. The reason I write that is that some solicitors are better than others (and some are totally useless!) at asking all the questions that really need to be asked. (e.g. if you leave something to Beneficiary A, the first thing any decent solicitor should ask is what you want to happen if Beneficiary A actually dies before you do).
So (before you go anywhere near to a solicitor's office) I suggest heading to your local library and getting hold of a copy of this book:
Amazon.co.uk User Recommendation
(It's in almost every library in the country - or you could simply buy it from Amazon anyway).
Then draft your own will. If you're 100% confident that you know what you're doing, you can go ahead and sign it in the presence of witnesses but it might be better to then take that draft to a solicitor and ask him/her to check it and tidy up any problems for you.
Please don't let a solicitor talk you into letting him/her be an executor; it's far better to appoint people that you know and trust. (They can still obtain professional help, with the costs coming from your estate, if they think that they'll need it).
If you use a solicitor to finalise your will you don't need to worry about finding any witnesses. The solicitor and one of his/her staff will do that job for you. If you decide to do it all yourself though, your witnesses can simply be any (non-beneficiary) adults and there's no need for any great formalities. (The witnesses just need to affirm that they've actually seen you sign your will).
My own will was signed and witnessed in a Tesco car park, with the witnesses simply being a couple of people I was working with on that day!