Personal information would be compromised as you said it, but at least if they were paying with Bitcoin, credit cards and bank details wouldn't be compromised. In the end that would save a lot of money to the banks, customers and Talk Talk.

For example, my previous bank in France was charging me 30 euros fee for every new credit card that had to be issued before an expiration date on the old one. This means if my credit card got compromised, I had to pay. Not to mention the damage that hackers can make to my bank account directly by using stolen credit card details.

Bitcoin would still make lives much easier.

True, but it also opens a new way to attack the customer. If your mail address is known as well as that you use bitcoin, you could be targeted with custom malware. Some of these phisihing mails are actually very good and hard to distinguish from the original, esp. after a breach.

E.g. paypal says "if we give your full name, you can be sure its legit", which is utter nonsense if you consider that PP is often tied to a mail address and in light of such a breach the information is easily available for the attackers. Many smart people I know fell for these kind of attacks, because the mail design was copied perfeclty, it had all the usual details and the attackers made the issue sound urgent. The attachment is (or at least looks like) a .pdf right, what could go wrong.

Dont get me wrong here I prefer more services accepting bitcoin payments, but it will not make the service miraculously secure or cause less issues for the customers in terms of a breach. The issues will just be different and it will take time to adjust to them.

The best defense against identity theft and the issues that follow it is very simple: dont gather information you do not must have to offer the service. Talk talk will certainly have to store your phone number if they sell you phone service, but do they need the name and (mail) address if you pay up front?

Blockchain.info is not extremely secure for payment systems. It does cause inconvenience if it requires regular subscription based payments, users would have to make payment manually if they don't want to prepay it. Using a POS system would eliminate the need to coding a page for the payments.

It could be implemented, and it would only require the customer to just give an email address for notification and a bitcoin address for receiving/sending transactions. Alao, it would be much easier on Talk Talk's part to integrate bitcoin as it will lessen their work storing and sorting out names and information regarding different users.

Many sites uses CC instead of Bitcoin as it's accepted widely. It would be impossible for any site to survive solely on using it as a payment method. Not that I support Paypal, but couldn't you implement it on the site and hackers would not be able to compromise user's info?

Bitcoin already is a secure form of payment if you'd ask me. The thing that you'll need to worry aboyt us the platform that you use and the way how they handle sensitive information.

I think DASH still has flaws, it's just like using a mixer or joinmarket.
You could look at Monero.