If by 'best' you mean cheapest then I wouldn't know as I tend to avoid the cheap providers (you get what you pay for with broadband). I would avoid the smaller resellers and go for a well-known, reliable provider. I have assumed that your parents will just surf the web and do email. I can recommend the following ISPs as good choices in no particular order: Zen (pricey but excellent rep), Newnet (good performance), Nildram, Eclipse, Pipex, BeThere. AOL may be a good choice even though I would avoid it like the plague for my purposes. There is one particular site which is the authoritative site on UK broadband - I do not know if I can post it here.
[edited by: lawman at 12:28 pm (utc) on Jan. 2, 2007]
I have been using Telewest Cable Broadband for more than five years now and it's a very reliable service. If cable is an option I would recommend that you go for it. I have a friend who has broadband through his telephone line and as I understand it this is much more unreliable.
Go for proven reliability because you will be their first port of call when there are problems ;)