Are there any mathematics or physics postgraduate courses (not taught courses) in the UK where you can continue a piece of research work you did whilst an undergrad? So you effectively do a project that maybe lasts a year(ish) which is productive but you would not do it for 3 years+ and receive a PhD?
In the UK it is possible to apply for an MPhil (Masters of Philosophy) degree (which is essentially a mini-PhD) or alternatively an MRes (Masters by Research) degree which is generally shorter.
A caveat: the MPhil may be interpreted as a botched PhD as the degree is often awarded to PhD candidates who don't cut the mustard or drop out. Don't let that put you off though.