I don't really understand the figures you have posted. You say the first TalkTalk bill is £38.82 and your regular monthly Shell bill was £26.49, which is a difference of £12.33, but you also mention an extra £16.60.
I would say though, if you are trying to work out a pro-rata service period, rather than looking at the date the payments come out of your bank account, you need to look at the service periods that the payments cover. For example, my Direct Debit payment is taken from my bank anywhere between roughly the 7th to the 10th of the month but the bill is actually produced at the start of the month and it is listed on the bill that the period of service covered is always the 1st to the 28/29/30/31st (depending on how many days in the month). If you look at your own first TalkTalk bill, you should be able to see what period is covered by the amounts they are charging you, and you would then need to work out what date you had already paid up to with your last Shell bill (I have no idea how their billing system works).
On a separate point, in some ways you never really fully left TalkTalk, since Shell used TalkTalk's network to deliver your services. The only difference was who you paid the bills to.
