Two things you need to establish - 1) that there is actually brick behind that soffit & 2) how far in those anchors go. If there's brick, then longer anchors of the same type will be fine; the next size up if you want them to withstand the next storm, though as the last one managed to take entire roofs off in Manchester, you are going to be hard-pressed to be proof against that. Those anchors ought to be stronger than the gutter brackets if they're in the brick far enough & the original hole tolerance was good.
The reasoning behind using a large collared plug is so you're not squeezing the soffit against the wall - as there's usually a gap between it & the wall it's fixed to - but it does mean you need longer fixings to get enough of it into the wall itself. I'd go with something an inch longer than the current fixings.
It's hard to tell from the picture whether those are countersunk or mushroom head; I'd always be swayed towards mushroom head on plastic, countersunk if over-tightened can break the fixing. Square or Torx drive are much easier to use than cross-head [Phillips/Pozidriv].