I think the biggest issue is how you're going to pay for such a second degree. You don't get funding from SFE for second degrees except in specific circumstances for specific courses (none of the courses you noted would be eligible for second degree funding). This is also even more complicated for Cambridge as for second degrees for home students they also charge college fees on top of the tuition fees and your usual accommodation etc costs, which are very steep (Oxford I believe does not levy college fees for home students for second degrees).
A masters even with no funding would end up being cheaper in most cases.