I don't think there's anything such as a 'better' provider out there - they'll all do very well right up until the point where they don't. You might be lucky, you might not.
GiffGaff get a thumbs up from me - not for any great reasons as their service just works for me, but because you're only ever - effectively - on a month long contract. You want to change provider at the end of the month ? No problem, just cancel the recurring charge and move on - no hassle, no grief.
They are a relatively 'bare bones' provider, so if you want to claim your free chocolottofrappocini coffee after every 50 dozen calls or you want free vouchers to the cinema that you'll never use - they're not the ones for you

They use the O2 network, and they're web based and if you have any problems they'll guide you towards the very useful GiffGaff community in the first instance to see if your answers can be found there.
On a side note - I had to deal with TalkTalk a few years ago to deal with a deceased person's account with them. The conversation went something like this:
Me : "Hi, I'd like to talk to someone about dealing with a deceased member of the family's account please"
TalkTalk : "Are you the account holder"
Me : "Errr, no"
TalkTalk : "Well I need to talk to the account holder first, please"
Me : "You can't. They're dead"
TalkTalk : "Ummm, I'm afraid I can't help you then"