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I need to know what activity there was on my phone on a specific date and time, is this possible?
It depends a bit how long ago.
If you log in to your My Vodafone account, and go to Plan Usage, Usage Breakdown, See All Usage, you can see your usage for the last 90 days (limited to 600 calls, texts and data sessions). As some of the long service SMS messages from Vodafone count as 3 or 4 items, the 600 limit may be well short of 90 days. Today I seem to go back to 6 December.
If that doesn't take you far enough back, your other option is a Subject Access Request under the DPA - see http://www.vodafone.co.uk/cs/groups/public/documents/webcontent/vftst031658.pdf but do note the provisos on the form relating to PAYG customers, especially if you haven't registered your number. The guidance notes on http://www.vodafone.co.uk/cs/groups/configfiles/documents/contentdocuments/vftst042750.pdf give further information.
I imagine it will all be slightly different from late May, when the GDPR comes in, not least that there won't be a charge for SAR, but I presume you can't wait that long.