UK Car Repair Questions? Ask a Mechanic for Answers ASAP
I'd agree that checking the fuel pressure should be the next step and considering fitting a new fuel filter as if only slightly blocked this can lower fuel supply pressure and choke the main pump, the pump will be more sensitive to this when its cold as diesel thickens considerably with low temperatures.
to check an individual injector then the only way to do this is to remove it from the engine and have it flow tested
this isn't that expensive often you can have all 4 done for about £40 and the flow testing can often be combined with ultrasonically cleaning which can restore the performance
an injector problem is possible, but I'd certainly replace the filter 1st as the next step