Cable Standards and Selection

Would other non BS cables be accepted in the UK and signed off  ?
Generally perfectly fine yes, but only if made to an equivalent standard - one offering the same level of insulation/ voltage ratings and conductor cross-section and in the cases of armoured cables, equivalent mechanical robustness, or 'de-scoped' and used in containment, as if soft skinned.

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"Sign off" also requires a design authority with sufficient knowledge of other countries standards to make an informed decision. You or whoever this falls to, may end up  with a large folder of datasheets. In general only stuff for the UK market is certified to the BS, so there is far more stuff 'out there' made to other standards.
 
and what are the implications in not following cable recommendations in table 4A3? 
You will need to request access to the cable maker's data, or generic standard data for that type of cable if made to another national or harmonized standard. Some intelligent read-across between cables of similar construction and use of the figures for something similar may be possible unless pushing tight against the maximum ratings.

Mike.

PS as an example for your 2XYRY-fl

try page 30 of this PDF   Nominal 0.6 / 1 kV  XLPE Insulation, steel wire Armour, PVC-Sheath tested to V  reads like it meets or exceeds the spec for SWA for example and has rather lower minimum  temperature, so if you have liquid nitrogen about it may be a better  choice. I'd be pretty happy using that wherever  the same size XPLE low smoke SWA would be accepted

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For the instrument flex  RE-2X(st)Y  try the Eland data available here.

Again nothing terrible just a PVC insulated and sheathed round cable. Consider rather like arctic flex.

The minimum active cable size is provided which meets the current-carrying capacity and the maximum voltage drop requirements.

Note that a cable size larger than this minimum is also acceptable and may be more economical in terms of electrical losses over its lifetime.

The table number used from British Standard BS : is provided with the result for your reference and checking of the results by you.

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