I feel sure Peter Layton is a definite possible for the sig on your vase.
The shape of the vase is similar to a shape I have but mine has a small neck and rim.
The flattened slightly off circular shape is the same
I don't know enough about his output to know whether he did pieces in this range - but mine is signed on the side and has a beautifully ground flat base rather than it being polished. However mine is an early piece I think done in the 80's if I recall and things and time move on in terms of ranges and design

I think it's worth writing an email to him to ask.
m