- The notice demands that i supply the details of the person who i think was driving the vehicle at the time
That is an unusual requirement. The requirement is usually to name the person who was driving at the time.
- The notice also states that the speed was 33mph (the location in the notice is in a 30 mph zone)
Does it mention an intention to prosecute the driver for exceeding the speed limit, or is that merely background information?
- am i legally obliged to respond confirming who was driving at the time?
Failure to do so is a criminal offence, which carries 6 points and a hefty fine.
- do they need to prove there was evidence of dangerous driving (swerving etc) or would the photo's be deemed sufficient evidence?
Presumably you have been living under a rock since 2003. Using a hand-held phone while driving has been a specific criminal offence for over 20 years! Until about 3 years ago, the use had to be for interactive communications, but the law was tightened up in (IIRC) 2022 to include any "use".
They would need to be able to prove that you were using it, but I would suggest that holding a phone while driving very much raises a presumption of use.