My understanding is that you would have to run the adiabatic calculations to be absolutely sure, but if you aren't using BS3036 fuses, a 1.0mm² CPC is unlikely to be an issue.
I suppose it is strictly true that one should undertake an adiabatic calculation, but that is equally true with a 1.5mm² CPC, and I've never heard of anyone undertaking such a calculation to confirm that the CPC of 2.5mm²/1.5mm² cable was adequate for a sockets circuit! I think that the reality is that the calculation, if performed for any credible circuit, will probably always indicate that a 1.0mm² CPC is more than adequate (and probably even with a BS3036 fuse).
Whilst an adiabatic calculation is, in itself, very simple to do, the problem usually is in ascertaining what is an appropriate value of I²t to use for the calculation. I'm very used to working with graphs, but I wouldn't say that I could determine, with any confidence, the appropriate value of I²t to use from a graph like the one below (for Wylex NSB MCBs)! Apart from anything else, the horizontal (PSC) axis only goes down to 400A, which means that if the circuit's Zs is more than about 0.58Ω (or 0.55Ω if one takes 'Cmin' into account), which is lower than one would commonly see, one's PSC is not even 'on the graph'!
Anyway, if one pulls a (seemingly credible **) value out of the air for I²t of, say, 1,000 A²s (incorrectly given as "A²/sec" on graph below), then that would seemingly translate to a minimum copper CPC CSA of about 0.27mm², and even if one assumed a very much higher I²t of 10,000 A²s, the minimum CPC CSA would seemingly only become about 0.87mm².
** if I understand the Wylex graph correctly, I²t would be less than 1,000 A²s for any circuit with a PSC less than 400A. Furthermore, looked at simplistically, that value of I²t could be looked at as MCB operation in 6.25 millisecs at a current of 400A, which not beyond credibility.
Kind Regards, john