There was actually a line cut from The Christmas Invasion that explained the estuary accent, where it’s shown that part of Rose’s personality has infected the new Doctor’s character.

‘It’s a shame they cut that!’ he exclaims, sounding genuinely peeved. 'That was the other reasoning behind it as well, this idea that Rose had imprinted on him and I think it made a nice sense, and it feeds into that whole close relationship that they’ve got and how that was unfolding.’

—  David Tennant on not using his own Scottish accent in DW (2006)
Filming Bad Wolf Bay

Graeme Harper discusses filming the Bad Wolf Bay scene in Doomsday with David and Billie (2006 article). 

Found and edited from bluevolvic here.

I’ve woken up far too early. Not the easiest day ahead. Both for Billie as an actress and Rose as a character, they’ve got the most harrowing, disturbing, and ultimately romantic scene to get though. She’s literally tearing herself up emotionally. It’s the end of her journey, and I don’t know quite how to do it.

I’m driving out to the main unit location. We are about to shoot Billie’s final scene in Doctor Who. Yet when i finish this block she and David have to shoot two more stories, which are due to appear earlier on in season two.

This is going to be quite a wrench for both of them. We’ve got a beautiful beach at a place called Southerndown. You can see right across the Bristol Channel. Somerset is on the horizon, but for purposes of our story this will be a beach in Norway.

Questions are racing though my head. ‘What’s the best way to approach shooting this?’…'Who do I film first? David or Billie?’ 'Is that going to put too much pressure on them if I offer them that choice?’

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